Question

State the following statement is true or false

"Determinant of a skew symmetric matrix is zero".
The above statement is True/False ?

• A. True
• B. False

Answer 1

The correct option is A True

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

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

$\Rightarrow |A|=-|A^T|$

We know that $|A^T|=|A|$

$\Rightarrow |A|=-|A|$

$\Rightarrow |A|=0$

Therefore the determinant of a skew symmetric matrix is zero

So the given statement is correct