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If a is a Skew Symmetric Matric of Order 3, Then Prove that Det A = 0 - CBSE (Science) Class 12 - Mathematics

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Question

If A is a skew symmetric matric of order 3, then prove that det A  = 0

Solution 1

If A is skew symmetric matric then `A^T = -A`

`:. |A| = -|A^T|`

|A| = - |A|

`=> 2|A| =  0`

`=>|A| = 0`

Solution 2

Let A be a skew-symmetric matrix of order 3.

Therefore, AT=−A

∴ `|A^T| = |-A| = |A|`

⇒ |A| = |(-1)A|

We know that, |kA|=kn|A|, where n is the order of the matrix

`=> |A| = (-1)^3 |A|`

`=> |A| = -|A|`

`=> |A| + |A| = 0`

`=> 2|A| = 0`

`=> |A| = 0`

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Solution If a is a Skew Symmetric Matric of Order 3, Then Prove that Det A = 0 Concept: Symmetric and Skew Symmetric Matrices.
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