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evaluate: |(a+x,y,z),(x,a+y,z),(x,y,a+z)...

evaluate: `|(a+x,y,z),(x,a+y,z),(x,y,a+z)|`

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The correct Answer is:
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We have `|(a+x, y, z),(x, a+y, z),(x, y, a+z)|=|(a, -a, 0),(0,a,-a),(x,y,a+z)|`
`[ ( :'R_(1)toR_(1)-R_(2)), "and"(R_(2)toR_(2)-R_(3))]`
`|(a,0,0),(0,a,-a),(x,x+y,a+z)|` `[ :' C_(2)toC_(2)+C_(1)]`
`=a(a^(2)+az+ax+ay)`
`=a^(2)(a+z+x+y)`
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