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Let A and B be two square matrices of th...

Let A and B be two square matrices of the same size such that `AB^(T)+BA^(T)=O`. If A is a skew-symmetric matrix then BA is

A

a symmetric matrix

B

a skew-symmetric matrix

C

an orthogonal matrix

D

an invertible matrix

Text Solution

Verified by Experts

The correct Answer is:
B
Let `C=BA`, then
`C^(T)=(BA)^(T)=A^(T)B^(T)`
`=-AB^(T)` (as A is skew-symmetric)
`=BA^(T)" "("as "AB^(T)+BA^(T)=O)`
`=B (-A)`
`=- BA=-C`
Therefore, C is skew-symmetric.
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