(a) Prove that the transpose of the sum of two matrices A and B is the sum of their transposes.
(b) Verify this is so when
A = [1 2 3] and B = [4 6 8]
[4 5 6] [5 7 9]
(c) Prove that if A is a square matrix then S = 1/2 (A -A^t) is skew-symmetric.
(d) Verify that this S is skew-symmetric when A = [4 3]
(e) Prove that if A is a square matrix with complex elements, then H = 1/2 (A + A^*) is hermitian.
(f) Verify that this H is hermitian when A = [1+i 4-3i]
Any help with any of these questions would be greatly appreciated!