1. The problem statement, all variables and given/known data Prove that if A is nonsingular then A^T is nonsingular and (A^T)^(-1) = (A^(-1))^T 2. Relevant equations (AB)^T = (B^T)(A^T) 3. The attempt at a solution Step 1: Multiply both sides by B^T B^T * (A^T)^(-1) = B^T * (A^(-1))^T B^T * (A^T)^(-1) = (A^(-1)*B)^T (A^(-1)*B)^T = (A^(-1)*B)^T I feel that my last step is wrong. Any suggestions would be helpful. I was also noticing that if I take just the right side of the equation and do this A^T*(A^(-1))^T = (A^(-1)*A)^T = I^T = I which suggests that the left side has to equal I if I multiply it by A^T as well so A^T*(A^T)^(-1) = I which makes sense just looking at it. Thanks!