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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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