If the system of equations `x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y` has a non-trivial solution show that `a^2+b^2+c^2+2a b c=1`

Explanation

We have given: the system of equations
`x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y`
has a non-trivial solution

Then we have to show that `a^2+b^2+c^2+2a b c=1`

Let

`A=|(-1,c,b),(c,-1,a),(b,a,-1)|`

And as we given that system has non trival solution

`implies |A|=0`

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