Question

State true or false:

The determinant of a skew-symmetric matrix is a perfect square if it's elements are integers.

• A. True
• B. False

Answer 1

The correct option is A True

Skew symmetric matrix means $A=-A^T$

Apply determinant on both sides , we get $|A|=-|A^T|$

$\Rightarrow |A|=0$

If the entries of the skew symmetric matrix are integers then the determinant will be a perfect square

Therefore the given statement is True