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MatrixLab
The matrix that undoes this one.
For a 2×2 matrix, the inverse is found by swapping the main diagonal, negating the other two entries (the adjugate), then dividing every entry by the determinant — no row-reduction needed at this size.
Multiplying a matrix by its inverse gives the identity matrix — this is exactly how systems of linear equations (Ax = b) are solved directly as x = A⁻¹b, and why a zero determinant means no inverse, and no unique solution, exists.
2×2 matrix inverse
Inverse
[[0.6, -0.7], [-0.2, 0.4]]
det = 10
What you entered
Determinant
4×6 − 7×2= 10Swap diagonal, negate off-diagonal (adjugate)
[[d, −b], [−c, a]]= [[6, -7], [-2, 4]]Divide every entry by the determinant
adjugate ÷ 10= [[0.6, -0.7], [-0.2, 0.4]]Result
Inverse: [[0.6, -0.7], [-0.2, 0.4]]
Multiplying this matrix by its inverse gives the identity matrix — the inverse "undoes" the transformation this matrix represents.