Multiply, add or subtract matrices, and find the determinant, inverse or transpose of a matrix of any size. Enter your values; the result updates as you type, with the method shown below.
About this calculator
This matrix calculator adds, subtracts and multiplies two matrices, and finds the determinant, the inverse and the transpose of a matrix A.
Type each matrix with one row per line and values separated by spaces, then choose the operation.
When to use it
- Linear algebra homework.
- Solving systems of equations.
- Computer graphics transformations.
- Checking a hand calculation.
How to read the result
A × B needs as many columns in A as rows in B; A + B needs the same size. The determinant and inverse need a square matrix.
A matrix with determinant 0 has no inverse.
Mistakes to avoid
- Multiplying matrices of incompatible sizes.
- Expecting A × B = B × A.
- Using commas inside numbers and as separators at once.
Formula
A × B, A ± B, det(A), A⁻¹, Aᵀ
Worked example
A = [2 1; 1 3], B = [1 2; 0 1]: A × B = [2 5; 1 5].
Frequently asked questions
How do I enter a matrix?
One row per line, numbers separated by spaces.
When is there no inverse?
When the determinant is 0.
Is A × B equal to B × A?
Usually not.
When is there no inverse?
When the determinant is 0.
What is the transpose?
Rows become columns.
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Results are estimates for information only. Check important figures with a professional.