If A is a skew-symmetric matrix of order 3, then prove that det A = 0.(CBSE 2017)

Given: A is a skew-symmetric matrix of order 3.

To Prove: det(A) = 0

Concept Used:

For a skew-symmetric matrix

A^T = -A

Taking determinant on both sides, we get-

|A^T| = |-A|

⇒ |A| = (-1)³|A|

[∵ the value of determinant remains unchanged if its rows and columns are interchanged.]

[∵ |kA| = kⁿ|A| where n is the order of matrix]

⇒ |A| = -|A|

⇒ 2|A| = 0

⇒ |A| = 0

Hence, If A is a skew-symmetric matrix of order 3, then |A| is zero.