How to prove a transpose matrix

How to prove a transpose matrix

Prove that if $A$ is a square matrix, then:
a) $A+ A^T$ is symmetric.
b) $A-A^T$ is skew-symmetric.
c) Use part (a) and (b) to show $A$ can be written as the sum of a
symmetric matrix $B$ and a skew-symmetric matrix $C$, with $A = B + C$.