Question

1. If B is a skew-symmetric matrix, write whether the matrix (ABA) is symmetric or skew

Answer 1

∵, B is a skew-symmetric matrix. Then,
B'=-B where B' denotes the transpose of the matrix B.
Now, (ABA')'
=(A')'B'A'
=AB'A'
=A(-B)A'
=-ABA'
∴, ABA' is a skew-symmetric matrix.

Answer 2

ya she's right. ♦

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