If A and B are symmetric matrices, then write the condition for which AB is also symmetric.

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If A and B are symmetric matrices, then write the condition for which AB is also symmetric.

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Given, A and B are symmetric matrices.

Then A^T = A, B^T = B .......(1)

Now,

(AB)^T

= B^TA^T

= BA [ Using (1)] ......(2).

Now will be symmetric if (AB)^T= AB i.e. we should have BA = AB.

This is the required condition. [ Using (2)]

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