Matrix Calculator guide
Matrix Calculator: Determinant, Inverse and Multiplication
Use our matrix calculator to find the determinant, inverse, transpose and rank, or add, subtract and multiply matrices, with a worked 2×2 example.
By the AllCalculator editorial teamUpdated 15 October 20262 min read
Matrices are grids of numbers used in further maths, physics, computer graphics and engineering. Our Matrix Calculator handles the common operations without the risk of an arithmetic slip.
How to use the calculator (Matrix Calculator)
- Choose the operation.
- Type matrix A row by row, with spaces or commas between values and semicolons between rows. For example, 1 2; 3 4 is a 2×2 matrix.
- For two-matrix operations, type matrix B too.
What it can do
- Determinant of a square matrix
- Inverse, if the determinant isn't zero
- Transpose, swapping rows and columns
- Rank and trace
- A + B and A − B, for matrices of the same size
- A × B, when A has as many columns as B has rows
- k × A and A to a power
A worked 2×2 example
For A = [4 7; 2 6]:
- Determinant: 4 × 6 − 7 × 2 = 10
- Inverse: swap the diagonal, change the signs of the others and divide by the determinant
- A⁻¹ = [0.6 −0.7; −0.2 0.4]
Multiplying matrices
Each entry of A × B is a row of A times a column of B, added up. For [1 2; 3 4] × [5 6; 7 8], the top-left entry is 1 × 5 + 2 × 7 = 19, and the full answer is [19 22; 43 50]. Matrix multiplication isn't commutative, so A × B usually isn't the same as B × A.
For other maths, try our Scientific Calculator or Complex Number Calculator.
Frequently asked questions
When does a matrix have no inverse?
When its determinant is 0. Such a matrix is called singular.
What size matrices can I use?
Any size for addition, multiplication and rank. Determinants and inverses need square matrices.
How do I type a 3×3 matrix?
Put three numbers in each row, separated by semicolons: 2 1 0; 1 3 1; 0 1 4.
Use the Matrix Calculator to check your homework or speed up longer calculations.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.