What matrix sizes are supported?

The tool supports 2×2, 3×3, and 4×4 square matrices. For operations that require two matrices (add, subtract, multiply) both matrices must be the same size. Determinant and Inverse work on a single matrix.

What happens if a matrix is singular?

A singular matrix has a determinant of zero and has no inverse. The tool detects this condition, reports the determinant as 0, and displays a clear error message instead of attempting an impossible calculation.

How is the determinant calculated?

The tool uses cofactor expansion (Laplace expansion) along the first row. Each step is shown: the minor sub-matrices, the cofactor signs, and the running total, so you can verify each stage of the calculation.

How is the matrix inverse found?

The inverse is computed via the adjugate matrix divided by the determinant. The working shows the matrix of minors, the cofactor matrix, the adjugate (transposed cofactor matrix), and finally each element divided by the determinant.

math Free No signup

Matrix Calculator

Perform matrix operations — add, subtract, multiply, transpose, determinant, and inverse — with step-by-step working.

Loading tool…

About this tool

Select a matrix size (2×2, 3×3, or 4×4) and fill in the grid cells for Matrix A and Matrix B. Choose an operation: Addition, Subtraction, Multiplication, Transpose, Determinant, or Inverse. Results are displayed as a formatted matrix grid. For Determinant and Inverse, the tool shows full cofactor-expansion working so you can follow every step. Errors are clearly reported for singular matrices, incompatible sizes, and non-square inputs.

How to use

1 Select the matrix size (2×2, 3×3, or 4×4) from the size selector.
2 Enter values into the Matrix A grid — and Matrix B if the operation requires two matrices.
3 Choose an operation: Add, Subtract, Multiply, Transpose, Determinant, or Inverse.
4 Click Calculate to see the result matrix and, for Determinant/Inverse, the step-by-step working.

Frequently Asked Questions

Related tools

Scientific Calculator

Full scientific calculator with trig, logarithms, powers, and history — runs entirely in your browser.

Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step working and visual fraction bars.

Percentage Calculator

Compute percentages, increases, decreases, tips, and percentage-of-total — six modes.