Matrix Operations on the TI-84: Add, Multiply, Inverse & Determinant

Master matrix math on your calculator with this matrix operations TI-84 guide: enter matrices, add and multiply them, and find determinants, inverses, and transposes — plus solve systems of equations.

Quick answer: Press 2ND + x⁻¹ to open the MATRIX menu, go to EDIT, pick a matrix like [A], set its size, and type your numbers. Then use MATRIX → NAMES to drop [A] into calculations: [A]+[B] adds, [A]*[B] multiplies, and MATRIX → MATH gives you det(, inverse with the x⁻¹ key, and transpose.

Entering a matrix on the TI-84

Everything matrix-related on the TI-84 Plus CE lives behind one menu: press 2ND + x⁻¹ (the key with MATRIX printed above it). You will see three tabs: NAMES (paste a stored matrix into a calculation), MATH (matrix operations like det(), and EDIT (type in a new matrix).

1. Press 2ND + x⁻¹ to open the MATRIX menu.
2. Arrow right to the EDIT tab and press ENTER on a matrix name, for example 1:[A].
3. Type the number of rows, press ENTER, then the number of columns, press ENTER. A 2×3 matrix has 2 rows and 3 columns.
4. Type each value, pressing ENTER after each one. The cursor moves across each row, then down to the next row.
5. Press 2ND + MODE (QUIT) to return to the home screen.

Your calculator can store ten matrices, named [A] through [J], each up to 99 rows by 99 columns (limited by available memory). To use a stored matrix in a calculation, press 2ND + x⁻¹, stay on the NAMES tab, choose the matrix, and press ENTER — it pastes [A] onto the home screen. You can try every step below on our free TI-84 calculator right in your browser. Practice every matrix operations TI-84 skill here.

Adding and subtracting matrices

Addition and subtraction only work when both matrices have exactly the same dimensions — you add or subtract matching entries. If the sizes do not match, the calculator throws an ERR:DIM MISMATCH error.

1. Store your matrices as [A] and [B] using the EDIT steps above.
2. On the home screen, paste [A], press +, paste [B], and press ENTER: [A]+[B].
3. For subtraction, use [A]−[B] the same way.

Not sure two matrices are the same size? Check with MATRIX → MATH → dim(: type dim([A]) and press ENTER to see its dimensions.

Multiplying matrices

Multiplication has its own rule: the number of columns in the first matrix must equal the number of rows in the second. A 2×3 matrix times a 3×2 matrix gives a 2×2 result. Order matters — [A][B] is usually different from [B][A].

1. Paste [A] onto the home screen.
2. Press × (multiply), paste [B], and press ENTER: [A]*[B].

If the inner dimensions do not line up, you will get ERR:DIM MISMATCH. Scalar multiplication is simpler: just type a number in front, like 3*[A], and every entry is multiplied by 3. A handy shortcut in any matrix operations TI-84 session.

Determinant, inverse, and transpose

These three live under MATRIX → MATH (press 2ND + x⁻¹, then arrow right to MATH):

• Determinant — choose 1:det(, paste your matrix, close the parenthesis, and press ENTER: det([A]). Determinants only exist for square matrices (same number of rows and columns).
• Inverse — paste [A] on the home screen, then press the x⁻¹ key and ENTER: [A]⁻¹. Only square, non-singular matrices have inverses; if the determinant is zero you will see ERR:SINGULAR MAT.
• Transpose — choose 2:ᵀ from the MATH tab, then paste the matrix: ᵀ([A]). This flips rows into columns.

The same MATH tab also holds identity( (builds an identity matrix of any size) and augment( (joins two matrices side by side) — both handy for solving systems. For the official keystroke reference, see Texas Instruments.

Solving a system of equations

Take the system 2x + 3y = 7 and x − y = 1. Store the coefficient matrix as [A] = [[2,3],[1,−1]] and the constants as [B] = [[7],[1]]. Then type [A]⁻¹[B] and press ENTER — the result [[2],[1]] tells you x = 2, y = 1.

The alternative is the augmented-matrix method: augment([A],[B]) followed by rref( (both under MATRIX → MATH). That is a bigger topic, so we gave it its own tutorial — see the dedicated RREF guide in our TI-84 guides hub. Bookmark this matrix operations TI-84 guide for exam day.

Matrix operations TI-84: frequently asked questions

Why do I get ERR:DIM MISMATCH when adding matrices?
The two matrices are different sizes. Addition and subtraction require identical dimensions — check both with dim( under MATRIX → MATH.

Why do I get ERR:SINGULAR MAT when finding an inverse?
Your matrix has a determinant of zero, so no inverse exists. Double-check the numbers you entered.

Can I find the determinant of a non-square matrix?
No. det( only works on square matrices. Recheck that you entered the right number of rows and columns in the EDIT screen.

How do I delete a matrix to free memory?
Press 2ND + + (MEM), choose 2:Mem Mgmt/Del, then 4:Matrix, highlight the matrix, and press DEL.

Should I solve systems with [A]⁻¹[B] or with rref(?
Both give the same answer. The inverse method is faster for 2×2 and 3×3 systems; rref( on an augmented matrix shows the reduced row-echelon form, which teachers often want to see. For the full rref walkthrough, see our TI-84 guides hub.