Scientific · Matrix

Matrix Calculator

Add, multiply, and find the determinant of matrices.

Matrix Calculator

Choose a size and an operation, fill in the matrix values, then select Calculate.

Size

Operation

Matrix A

Matrix B

How this is calculated

Addition combines matrices of the same size, element by element. Multiplication takes the dot product of each row of A with each column of B. The determinant of a 2×2 matrix is ad − bc; for 3×3, it's computed by cofactor expansion along the first row. A worked breakdown of the determinant calculation is shown below the result.

Examples

For A = [1, 2; 3, 4] and B = [5, 6; 7, 8]: A + B = [6, 8; 10, 12], A × B = [19, 22; 43, 50], and the determinant of A is 1×4 − 2×3 = −2.

About this calculation

These are the standard linear algebra operations taught in introductory matrix algebra, restricted here to square matrices (2×2 or 3×3) of the same size for addition and multiplication.

Related tools

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Frequently asked questions

Why only 2×2 and 3×3 matrices?

These cover the most common cases for learning and everyday use while keeping the input grid simple. Larger or non-square matrices are out of scope for this calculator.

Why is Matrix B hidden for the determinant operation?

A determinant is a property of a single square matrix — Matrix B isn't used, so it's hidden to keep the workspace focused.