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Using the property of determinants and w...

Using the property of determinants and without expanding, prove that:`|[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0`

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Given `|[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|`
`|[a,b,c],[ b,c ,a ],[c ,a,b]|-|[b,c,a],[ c,a ,b ],[a ,b,c]|`
By finding the determinant of each we get
i.e., `=a(cb-a^2)-b(b^2-ca)+c(ba-c^2)-b(ac-b^2)+c(c^2-ab)-a(cb-a^2)`
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