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If B is a symmetric matrix, write whe...

If `B` is a symmetric matrix, write whether the matrix `A B\ A^T` is symmetric or skew-symmetric.

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Given: B is a skew- symmetric matrix
`implies B^T=-B......(i)`
Now
`(ABA^T)^T=(A^T)^TB^TA^T`
{As `(AB)^T=B^TA^T`}
`implies (ABA^T)^T= AB^TA^T`
{As `(A^T)^T=A`}
Now from (i) we get
...
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