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Let A be a square matrix of order 3xx3, ...

Let A be a square matrix of order `3xx3`, then `|k A|`is equal to(A) `k|A|` (B) `k^2|A|` (C) `K^3|A|` (D) `3k |A|`

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The correct Answer is:
( c)
`A=|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|`
`kA=|{:(ka_(1),ka_(2),ka_(3)),(kb_(1),kb_(2),kb_(3)),(kc_(1),kc_(2),kc_(3)):}|`
`|kA|=|{:(ka_(1),ka_(2),ka_(3)),(kb_(1),kb_(2),kb_(3)),(kc_(1),kc_(2),kc_(3)):}|`
`=k^(3)|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|=k^(3).|A|`
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