Matrix Operations

Matrices are rectangular arrays of numbers that power linear algebra — solving systems of equations, transforming geometry, and compressing data. This matrix calculator handles the core operations for 2×2 and 3×3 matrices.

The Operations

Addition combines element-by-element; multiplication is the row-by-column dot product; the determinant is a single number encoding invertibility and scaling; the inverse (when it exists) undoes the matrix; the transpose flips rows and columns. Together they cover most coursework and quick engineering checks.

Reading the Results

If the determinant is zero, the matrix is singular — no inverse exists and the system it represents has no unique solution. Otherwise A⁻¹ = adj(A)/det(A), computed here via cofactor expansion. Use the row-magnitude chart to eyeball which rows dominate the result.