matrix help?

Question

suppose matrix A is non singular show that [A^T]^ -1= [A^ -1]^T
which T is transpore ^-1 is inverse
please show work thanks in advance

Answer 1

you can choose 2x2 work very easy more than 4x4
you can do on left side and right side at the same time then compare two sides together.\good luck

Answer 2

Just set up a 4x4 matrix of variables and do your own math
to find the inverse just use an augmented matrix and row reduction