Implicit Function Theorem ...Tricky Proof on matrices!? 1. The problem statement, all variables and given/known data Implicit Function Theorem ... Tricky Proof on matrices!? Show with the Implicit Function Theorem, that an n x n matrix B, can be solved for as a continuous differentiable function of a matrix A (which is n x n), from the equation BAB = id, given that || A - id || is sufficiently small. Can someone outline the solution to this problem? I don't know how to proceed with the proof. Can you please show all the steps of the proof?