If the system of linear equations `x=cy+bx`, `y=ax+cz`,`z=bx+ay` has a non trivial solution show that `a^2+b^2+c^2+2abc=1`

Explanation

It is known from solution of equation that a equation will have no trivial solution when the product if matrix is zero

When `x=cy+bx,`
thn,`x=1,y=-c,z=-b`

When `y=ax+cz,`
then,`x=-a,y=1,x=-c`

When `z=bx+ay`,then,
`x=-b,y=-a,z=1`

expanding in matrix form :--

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