If A and B are symmetric matrices then BA

Engineering

Mathematics

Special Type of Square Matrices

Symmetric and Skew Symmetric Matrices

Question

If A and B are symmetric matrices then BA – 2AB is a _______.

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A and B are symmetric matrices.

∴ A' = A, B' = B ⋯⋯(1)

Now, (BA – 2AB)' = (BA)' – (2AB)' = (BA)' – 2(AB)' ⋯ {∵ (kA)' = k(A), k = scalar }

∴ (BA – 2AB)' = A'B' – 2B'A' ⋯ {∵ (AB)' = B'A'}

∴ (BA – 2AB)' = AB – 2BA = – (2BA – AB) ⋯⋅( from (1))

Hence, If A and B are symmetric matrices then

BA – 2AB is neither symmtric nor skew symmetric marix