Since, A is a skew symmetric matrix
∴AT=−A
⇒|AT|=|−A|
⇒|−A|=(−1)n|A|
where n is the order.
∴|−A|=(−1)3|A|
=−|A|
Substituting in (i),
|AT|=−|A|
⇒−|A|=|AT|
We also know for any matrix.
|A|=|AT|
replacing in (ii)
∴|A|=−|A|
⇒2|A|=0
⇒|A|=0