If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______

Engineering

Mathematics

Algebra of Matrices

Special Type of Square Matrices

Question

If A and B are symmetric matrices of same order, then AB is symmetric if and only if _______.

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A and B are symmetric matrices of same order.

∴ A' = A, B' = B

∴ (AB)'

= B'A' = BA

So, for AB to be symmetric BA must be equal to AB

So, If A and B are symmetric matrices of same order, then AB is symmetric if and only if AB = BA