Matrices are common in algebra, precalculus and systems of equations. This guide explains how to enter matrix dimensions, fill matrix values and perform common matrix operations.
Open the matrix editor
Use the matrix menu to choose a matrix name such as [A], [B] or [C]. Edit the dimensions first, such as 2×2 or 3×3, then enter each value.
Dimensions matter. A 2×3 matrix and a 3×2 matrix contain different arrangements and cannot always be used in the same operations.
Add and subtract matrices
Matrices can be added or subtracted only when they have the same dimensions.
If you get a dimension error, compare rows and columns of both matrices. They must match exactly for addition or subtraction.
Multiply matrices
For multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.
The result has the row count of the first matrix and the column count of the second matrix.
Inverse matrices
A square matrix may have an inverse if its determinant is not zero. Use the inverse key or menu operation after entering the matrix.
If the determinant is zero, the matrix is singular and does not have an inverse.
Determinants
The determinant is a number associated with a square matrix. It helps determine whether a matrix has an inverse and is used in many algebra applications.
Only square matrices have determinants. If your matrix is not square, determinant operations do not apply.
Quick reference table
| Operation | Requirement |
|---|---|
| A + B | Same dimensions |
| A - B | Same dimensions |
| A × B | Columns of A equal rows of B |
| A⁻¹ | A is square and determinant is not zero |
| det(A) | A is square |