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
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
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Correct Answer - 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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