Inverse of a 2×2 Matrix

Swap the diagonal, negate the off-diagonal, divide by the determinant.

[a c b d]^{- 1} = \frac{1}{a d - b c} [d - c - b a]

Variables

The inverse satisfies $A A^{- 1} = I$ . For larger matrices, row-reduce $[A ∣ I]$ to $[I ∣ A^{- 1}]$ .

$[2113]^{- 1} = \frac{1}{5} [3 - 1 - 1 2]$ .

Matrix determinant, inverse, transpose, RREF, rank, eigenvalues, multiplication and addition with steps.

Determinant of a Matrix

Scalar that tells whether a matrix is invertible.