The system of linear equations x+λy−z=0,  λx−y−z=0,  x+y−λz=0has a non-trivial solution for

The system has non-trivial solution ⇒Δ=0⇒1λ-1λ-1-111-λ=0    ⇒λ+1-λ-λ2+1-λ+1=0 ⇒λ(λ2−1)=0⇒λ=0,    ±1∴λ has three values