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If a , b , c are non-zero real numbers ...

If `a , b , c` are non-zero real numbers and if the system of equations `(a-1)x=y+z` `(b-1)y=z+x` `(c-1)z=x+y` has a non-trivial solution, then `ab+bc+ca` equals to (A) `abc` (B) `a^2 - b^2 + c^2` (C) `a+b -c` (D) None of these

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`(a-1)x-y-z = 0`
`x- (b-1)y + z= 0`
`x + y - (c-1) z = 0`
`D= |(a-1, -1,-1),(1, -b+1), 1), (1,1, -c+1)|`
`D=0`
`D= |(a-1,-a,-a),(1,-b,0),(1,0,-c)|`
`=> -a(0+b) - c(-ab+b+a) `
`= -ab + abc-b - ac`
...
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