Chapter 1.4, Problem 11E

Let C be nonsymmetric $n\times n$ matrix. For each of the following, determine whether the given matrix must necessarily be symmetric or could be nonsymmetric:

(a) $A=C+C^T$

(b) $B=C-C^T$

(c) $D=C^{T}C$

(d) $E=C^{T}C-C{C}^T$

(e) $F=(I+C)(I+C^T)$

(f) $G=(I+C)(I-C^T)$