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Singular and Non Singular Matrices

If A and B ar...

Question

If $A$ and $B$ are symmetric matrices, then $A B A$ is

A

Symmetric matrix

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B

Skew-symmetric

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C

Diagonal matrix

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D

Scalar matrix

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Solution

The correct option is A Symmetric matrix
$A^{T} = A$ and $B^{T} = B$
$(A B A)^{T} = A^{T} B^{T} A^{T} = A B A$

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