Q. 55.0( 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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