The correct option is B −2
Here, D=∣∣
∣∣α111α111α∣∣
∣∣
⇒D=(α−1)2(α+2)
Taking D=0
⇒(α−1)2(α+2)=0
⇒α=1,α=−2
At these values of α, system can have either no solution or infinitely many solution.
For α=1, equations takes the form x+y+z=0
Hence, infinitely many solution for α=1.
For α=−2,
D1=∣∣
∣∣−311−3−21−31−2∣∣
∣∣
D1=27≠0
So, D=0, at least one D1≠0
Hence, system has no solution for α=−2