1. The problem statement, all variables and given/known data A = [ 1 0 1 0 2 3 0 6 0 5 −5 0 0 0 0 2 ] Prove that if there is a 4 × 4-matrix B such that A · B = I4, then B = A−1. 2. Relevant equations 3. The attempt at a solution First of all I got the determinant of the matrix A which is -10 I'm just wondering if there's a shortcut to this problem, I began multiplying the matrix A by B (B is not given, so I used b11, b22, etc. I could equate each term in A*B with the corresponding entry in the identity matrix, which will give loads of equations which I guess could be used to solve for the b's and gives me something which I could multiply by A to get the Identity matrix. I guess this would prove it but this will take me ages, and this is an exam question so I'm guessing there is a simpler way. If I got this question in an exam I wouldn't dream of doing this, it would take way too long. I'd probably just say that since its determinant is non-zero it must have an inverse and any matrix multiplied by it's inverse is the Identity matrix Still I'd appreciate if anybody has any other quick way(s)of proving this. Thanks!