So, if I understand, you wonder if equality holds.
Multiply both sides by : .
On the right-hand side of the equation you have identity matrix: .
And left-side, , equals identity matrix .
Let A be an nxn invertible matrix.
I can't figure out how to prove the following:
t(A^-1) = (t(A))^-1. So the transpose of A inverse is equal to the inverse of A transpose.