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

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 .

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