Dividing by a matrix sounds impossible — until you meet its inverse. For ordinary numbers, the inverse of 5 is 1/5 because 5 × 1/5 = 1; for a square matrix A, the inverse A⁻¹ is the matrix that satisfies A × A⁻¹ = I, the identity matrix. Multiply both sides of a matrix equation by the inverse and the matrix "divides away," which is how engineers solve entire systems of equations in one stroke and how computer graphics undo rotations and scalings. The catch: only square matrices with a nonzero determinant have inverses — a zero determinant means the matrix squashes space flat, and no undo exists.

The 2×2 case has a famous shortcut: swap the diagonal entries, flip the signs of the off-diagonal entries, and divide everything by the determinant (ad − bc). For [[4, 7], [2, 6]], the determinant is 24 − 14 = 10, and the inverse is [[0.6, −0.7], [−0.2, 0.4]]. This calculator evaluates the inverse computation: enter your matrix values and read the computed result, then verify by multiplying the original and the inverse — you should get the identity matrix, 1s on the diagonal and 0s elsewhere. That self-check is the whole game: if A × A⁻¹ ≠ I, something went wrong.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Inverse Matrix Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.