Question

Suppose $A$ and $B$ are two square matrices of same order. If $A,B$ are symmetric matrices and $AB=BA$ then $AB$ is

• A. a symmetric matrix
• B. a skew symmetric
• C. a scalar matrix
• D. a triangular matrix

Answer 1

The correct option is A a symmetric matrix

$(AB{)}^T=B^T{A}^T=BA=AB\Rightarrow (AB{)}^T=AB$

So that means the product of the matrices $AB$ is a symmetric matrix.

Option A is the correct answer.