What a matrix inverse is
The inverse of a matrix A, written A⁻¹, is the matrix that when multiplied by A gives the identity matrix. Not every matrix has an inverse; a matrix only has one if its determinant is not zero.
The formula used
For a 2×2 matrix [[a, b], [c, d]], the determinant is det = ad – bc. When the determinant is nonzero, the inverse is (1/det) × [[d, -b], [-c, a]]. If the determinant equals zero, the matrix is called singular and has no inverse.
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Last reviewed August 2026