In your Command Window, type this:
You'll see elements of A_T and A_1 are essentially the same, but the last digit may not be exactly the same.
You're using two different methods on A that have the same theoretical answer (A' and A^-1). Both calculations are subject to machine error since they only track 64 bits of information. Since A' and A^-1 use different algebra to arrive at the same answer, they end up with slightly different 64-bit rounded answers.
You can check for equality up to a given threshold like this:
threshold = 1e-10;
tf = all(abs(A_T(:) - A_1(:))<=threshold);