Free Online Matrix Calculator

1. Choose 2×2 or 3×3 from the size selector.
2. Pick the operation: determinant, transpose, or A × B.
3. Fill in matrix A (and matrix B for multiplication).
4. Read the scalar (determinant) or grid (transpose / product) result.

Matrices represent linear transformations, systems of equations, and grid-shaped data. For 2×2 and 3×3 square matrices the three most common operations are: determinant (a scalar summary, zero when the matrix is singular), transpose (rows become columns), and matrix product (composition of two transformations).

This tool focuses on 2×2 and 3×3 because they cover almost all undergraduate course exercises, classical-mechanics problems, and 2D/3D graphics math. Determinant uses the direct ad − bc formula for 2×2 and cofactor expansion along the first row for 3×3. Multiplication follows the standard row-by-column dot-product rule and only operates on matrices of the same size.

All entries can be decimals including negatives. Determinant prints as a single scalar; transpose and product render as a clean grid below the inputs.