Prove the following statements or provide counterexamples to show they are not true. a. The product of

Question:

Prove the following statements or provide counterexamples to show they are not true.
a. The product of two symmetric matrices is symmetric.
b. The inverse of a nonsingular symmetric matrix is a nonsingular symmetric matrix.
c. If A and B are n × n matrices, then (AB)t = AtBt .