Given systems of equations can be rewritten as -x +cy +by =0, cx -y + az =0 and bx+ ay-z =0
Above system of equations are homogeneous equation. Since x,y and z are not all zero, so it has non-trivial solution.
Therefore, the coefficient of determinant must be zero.
`therefore |{:(-1, c, b),(c, -1, a),(b, a, -1):}| =0`
`rArr -1(1-a^(2)) -c(-c-ab) + b(ca+b) =0`
`rArr a^(2) + b^(2) +c^(2) +2abc-1 =0`
`rArr a^(2) + b^(2) + c^(3) + 2abc =1`
