Question

If A and B are symmetric matrices of the same order, then
(a) AB is a symmetric matrix
(b) A – B is askew-symmetric matrix
(c) AB + BA is a symmetric matrix
(d) AB – BA is a symmetric matrix

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Answer 1

Answer:

Complete step-by-step answer:

Given that A and B are symmetric matrices; which means that, A' = A and B' = B. Also we are given that, AB = BA. Hence AB is symmetric. Now because A is symmetric, then A−1 is also symmetric.

Answer 2

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• (a) AB is a symmetric matrix

Step-by-step explanation:

Given that A and B are symmetric matrices; which means that, A' = A and B' = B. Also we are given that, AB = BA. Hence AB is symmetric. Now because A is symmetric, then A−1 is also symmetric.

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