Question

Show that the determinant of a skewsymmetric matrix of order three is always zero.

Maths:1a question

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Answer 1

This is easy if you observe a property of matrices

and determinants.

1. Determinant is invariant under

transposition that is determinant of a

matrix A and its transpose are the same.

2. For odd size square matrices, Determinant

of -A

-Determinant of A

3. For a skew symmetric matrix, transpose

of A = -A.

So, using the above three facts, it is easily seen that

the determinant of a skew symmetric matrix of

order 3 should be 0.

Hope it helps...

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