How to find a determinant, inverse and eigenvalues of a matrix on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
On the fx-CG50: MENU → 1 (RUN-MATRIX) → F3 (MAT/VCT).On the TI-84 Plus CE: 2nd x⁻¹ (MATRIX) → EDIT.On the TI-Nspire CX II: menu → Matrix & Vector → Determinant.
Enter a matrix, then the determinant, inverse, powers and (on the TI-Nspire) eigenvalues. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
AI HL: matrix arithmetic, inverses to solve systems, transition matrices and steady states for Markov chains, and eigenvalues/eigenvectors (diagonalisation). Matrices are not in the AA syllabus (AA HL solves systems of equations with the equation solver instead).
Practise it: HL AI matrices · HL AI Markov chains · HL AI eigenvalues.
Which IB course and paper
| Course | GDC papers | What you use it for |
|---|---|---|
| AA SL | Not in the syllabus | — |
| AA HL | Not in the syllabus | — |
| AI SL | Not in the syllabus | — |
| AI HL | Papers 1, 2 and 3 | Matrix arithmetic, inverses, transition matrices (Markov chains) and eigenvalues. |
A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.
Topic notes: Matrices (AI HL) · Markov chains and transition matrices (AI HL) · Systems of linear equations and Gaussian elimination (AI HL).
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Matrices on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
Watch the key presses on the fx-CG5022 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- MENU 1 (RUN-MATRIX), then F3 (MAT/VCT) to open the matrix list.
- Highlight Mat A, EXE, set m = 2 EXE and n = 2 EXE, type the entries with EXE after each, then EXIT twice.
- Determinant: OPTN F2 (MAT/VCT) F3 (Det), then F1 (Mat) ALPHA X,θ,T (A), EXE.
- Inverse: F1 (Mat) ALPHA X,θ,T (A) SHIFT ) (x⁻¹) EXE. Powers: Mat A ^ 10 for a Markov chain after 10 steps.
- Eigenvalues: there is no eigenvalue command. Find the characteristic equation det(A − λI) = 0 (for a 2 × 2 matrix, λ² − (trace)λ + det = 0) and solve it in EQUATION → POLYNOMIAL.
- Steady state of a Markov chain: raise the transition matrix to a large power (Mat A ^ 50) and check the columns (or rows) stop changing, or solve (T − I)s = 0 with Σs = 1.
- Matrices up to 99 × 99 are possible, but the IB only needs small ones.
Matrices on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
Watch the key presses on the TI-84 Plus CE17 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 2nd x⁻¹ (MATRIX) → EDIT → 1: [A]. Set 2 × 2 and type the entries.
- 2nd mode (QUIT). Determinant: 2nd x⁻¹ → MATH → 1: det(, then 2nd x⁻¹ → NAMES → 1: [A], ) enter.
- Inverse: [A] x⁻¹ enter (use ►Frac from math for fractions). Powers: [A]^10.
- Eigenvalues: no built-in command; solve λ² − 5λ + 5 = 0 (PlySmlt2 or the Solver).
Matrices on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS (the CX II CAS is a different model: check the exam rules before using one).
- Calculator page: templates → the 2 × 2 matrix template, type 2, 1, 1, 3, then ctrl var (sto→) a enter to store it as a.
- det(a) enter (menu → Matrix & Vector → Determinant).
- a^−1 enter for the inverse; a^10 for powers.
- eigVl(a) gives the eigenvalues and eigVc(a) the eigenvectors (unit length) (menu → Matrix & Vector → Eigenvalues / Eigenvectors).
- eigVc gives normalised eigenvectors: scale them to whole numbers if the question expects that.
For teachers: Show on the board Print a keystroke card Teaching GDC skills
Quick answers
How do I enter a matrix on the fx-CG50?
MENU 1 (RUN-MATRIX), then F3 (MAT/VCT) to open the matrix list. Highlight Mat A, EXE, set m = 2 EXE and n = 2 EXE, type the entries with EXE after each, then EXIT twice.
How do I enter a matrix on the TI-84 Plus CE?
2nd x⁻¹ (MATRIX) → EDIT → 1: [A]. Set 2 × 2 and type the entries.
How do I enter a matrix on the TI-Nspire CX II?
Calculator page: templates → the 2 × 2 matrix template, type 2, 1, 1, 3, then ctrl var (sto→) a enter to store it as a.
Worked example
A = (2 1; 1 3). Find det A, A⁻¹ and the eigenvalues of A. Also find det of (1 2 0; 3 −1 4; 2 0 1).
Answers (checked with Python)
det A = 5. A⁻¹ = (0.6 −0.2; −0.2 0.4). Eigenvalues: λ² − 5λ + 5 = 0, so λ = 1.38197 and 3.61803. The 3 × 3 determinant is 9.
Now try it on an exam-style question
Use the keystrokes above on IB-style matrices questions. Free to try, no sign-up.
Common calculator mistakes
- Entering the matrix by columns instead of rows.
- Multiplying in the wrong order: AB ≠ BA; a transition matrix acts on the state vector from the correct side (check the course's convention).
- Inverse of a singular matrix (det = 0): the calculator gives an error, which usually means a mistake or a system with no unique solution.
- Rounding a transition matrix before raising it to a power.
- Steady state from a high power: say which power you used and check the next power gives the same values to 3 s.f.
- Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).
If you get an error
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:DIM MISMATCH, ERR:SYNTAX, ERR:DATA TYPE
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:DIM MISMATCH Lists or matrices in the same operation have different sizes (TI's example: multiplying two lists with different numbers of elements). Check: L1 and L2 with different numbers of values (one value missed or typed twice), a frequency list of the wrong length, or matrices whose sizes cannot be multiplied. Fix: Make the lists the same length, or check the size of each matrix.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
ERR:DATA TYPE An argument is the wrong type, such as a complex number where a real number is needed, or a matrix stored to a list. Check: A complex result used in a real-only command, or a list and a matrix mixed up. Fix: Use the type the command expects.
TI-Nspire CX II: Domain error, Dimension mismatch, Syntax error
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Dimension mismatch Two or more arguments must have the same dimension and do not (TI's example: [1,2]+[1,2,3]). Check: Lists of different lengths in a statistics command, or vectors or matrices of different sizes. Fix: Make the lists, vectors or matrices the sizes the operation needs.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
Do it in Desmos
Not in the exam. Desmos is not an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- Matrices are in the separate Desmos Matrix Calculator (desmos.com/matrix): det, inverse and powers, but not eigenvalues.
- In the graphing calculator you can see the eigenvalues as the zeros of the characteristic polynomial: plot y = x² − 5x + 5 (trace 5, det 5) and click the x-intercepts.
Open desmos.com/calculator (free, in any browser) and type:
y=x^{2}-5x+5
Questions
Can I use a calculator for matrices in the exam?
In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.
What are the fx-CG50 keystrokes for matrices?
MENU 1 (RUN-MATRIX), then F3 (MAT/VCT) to open the matrix list. Then Highlight Mat A, EXE, set m = 2 EXE and n = 2 EXE, type the entries with EXE after each, then EXIT twice. Then Determinant: OPTN F2 (MAT/VCT) F3 (Det), then F1 (Mat) ALPHA X,θ,T (A), EXE. The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.
How do I enter a matrix on the fx-CG50?
MENU 1 (RUN-MATRIX), then F3 (MAT/VCT) to open the matrix list. Highlight Mat A, EXE, set m = 2 EXE and n = 2 EXE, type the entries with EXE after each, then EXIT twice.
How do I enter a matrix on the TI-84 Plus CE?
2nd x⁻¹ (MATRIX) → EDIT → 1: [A]. Set 2 × 2 and type the entries.
How do I enter a matrix on the TI-Nspire CX II?
Calculator page: templates → the 2 × 2 matrix template, type 2, 1, 1, 3, then ctrl var (sto→) a enter to store it as a.
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the models shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.