A is skew-symmetric of order 3, write the value of |A|.

Question

Philoid · Accepted Answer

Since A is a skew-symmetric matrix, Therefore

A^T=-A

Taking determinant both sides

|A^T|=|-A|

Using |A^T|=|A| and |λA|=λ^m|A| where m is the order of A

|A|=(-1)³|A|

=-|A| or 2|A|=0

Hence, |A|=0