(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]

[2 1]

(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]

[2-i 3+2i]

Any help with any of these questions would be greatly appreciated!