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Without expanding or evaluating show tha...

Without expanding or evaluating show that `|[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0`

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Given
`D=|[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|`
`D=|[0 , a-b , a-c] , [b-a, 0 , b-c] , [c-a , c-b , 0]|=-D`
Thus it is an skew-symmetric matrix
And we know determinant of a skew-symmetric matrix of odd order is zero
...
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