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Question

If A is a skew-symmetric matrix, then A2 is a ___________ matrix.

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Solution


It is given that, A is a skew-symmetric matrix.

AT=-A .....(1)

Now,

A2T

=AAT

=ATAT [For any matrices X, Y, (XY)T = YTXT]

=-A-A [Using (1)]

=A2

Since A2T=A2, so the matrix A2 is a symmetric matrix.

If A is a skew-symmetric matrix, then A2 is a __symmetric__ matrix.

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