If |{:(a,b,c),(l,m,n),(p,q,r):}|=2, then...

If `|{:(a,b,c),(l,m,n),(p,q,r):}|=2`, then what is the value of the determinant `|{:(6a,3b,15c),(2l,m,5n),(2p,q,5r):}|`?

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The correct Answer is:

Let `|{:(a,b,c),(l,m,n),(p,q,r):}|=2`
Consider `|{:(6a,3b,15c),(2l,m,5n),(2p,q,5r):}|=2 xx 5|{:(3a,3b,3c),(l,m,m),(p,q,r):}|`
`= 10 xx 3|{:(a,b,c),(l,m,n),(p,q,r):}|`
`=30|{:(a,b,c),(l,m,n),(p,q,r):}|=30 xx 2 = 60`

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