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Without expanding prove that: |x+y y+...

Without expanding prove that: `|x+y y+z z+x z x y1 1 1|=0` .

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The correct Answer is:
Proved
`[[x+y,y+z,z+x],[ z, x, y],[1, 1, 1]=0`

Applying `R1​→R1​+R2`​, we get,

`[[x+y+z, x+y+z, y+z+x],[ z, x, y],[1, 1 ,1]=0`
`= (x+y+z)`

`[[1, 1, 1],[ z, x, y],[1, 1, 1]=0`

`=(x+y+z)×0=0`
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