Q. 174.2( 6 Votes )

If A is a skew-sy

Answer :

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

To Prove: det(A) = 0

Concept Used:

For a skew-symmetric matrix


AT = -A

Explanation:

Taking determinant on both sides, we get-


|AT| = |-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.

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