Pick a matrix size, enter the values, and get the inverse instantly — or a clear singular-matrix message if it doesn’t have one.
Matrix Inverse Calculator
How It’s Calculated
For a 2×2 matrix [[a,b],[c,d]], the inverse is (1/det) × [[d,−b],[−c,a]]. For a 3×3 matrix, this calculator builds the cofactor matrix, transposes it to get the adjugate, and divides every entry by the determinant. If the determinant is 0, there is no inverse — the matrix is called singular, and this calculator tells you that directly rather than dividing by zero.
Worked Example
For A = [[2,1],[1,1]]: det(A) = (2×1) − (1×1) = 1. A⁻¹ = (1/1) × [[1,−1],[−1,2]] = [[1,−1],[−1,2]]. Check: A × A⁻¹ should give the identity matrix.
Frequently Asked Questions
Q: Why does a matrix sometimes have no inverse?
Whenever its determinant is exactly 0. Such a matrix is called singular, and geometrically it collapses space into a lower dimension — there’s no way to reverse that.
Q: How can I check my inverse is correct?
Multiply the original matrix by the inverse you calculated — the result should be the identity matrix (1s on the diagonal, 0s elsewhere). Use the Matrix Calculator to check.
Inverses build directly on Determinants — the chapter covered right after Matrices in 2nd PUC. Read the Matrices chapter guide →