1.

Write the value of the following determinant `|(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|`

Answer» `|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|`
Applying `R_1->R_1+R_2+R_3`
`=|[0,0,0],[b-c,c-a,a-b],[c-a,a-b,b-c]|`
Here, all elements in first row are `0`.
`:.` Value of the determinant is `0`.
`=>|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]| =0`


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