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Find the determinant of the matrix [{...

Find the determinant of the matrix
`[{:(a,b,c),(b,c,a),(c,a,b):}]`

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If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin B. sin C, then find the valueof determinant |{:(a,b,c),(b,c,a),(c,a,b):}|.

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If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin B. sin C, then find the valueof determinant |{:(a,b,c),(b,c,a),(c,a,b):}|.

Using properties of determinants, prove that |{:(,a,b,b+c),(,c,a,c+a),(,b,c,a+b):}|=(a+b+c) (a-c)^2