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Using properties of determinants , prove...

Using properties of determinants , prove that,
`|{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc)`
and hence show that, `|{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2`

Text Solution

Verified by Experts

The correct Answer is:
`-(a^3+b^3+c^3-3abc)` (ii) `(a^3+b^3+c^3-3abc)^2`
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