The system of linear equations:
x+y+z=2
2x+3y+2z=5
2x+3y+(a^2-1)z=a+1

Has infinitely many solutions for a=4
Is inconsistent when |a|=√3
Has a unique solution for |a|=√3
Is inconsistent when |a|=4

The correct option is B Is inconsistent when |a|=√3
D = |1 1 1|
|2 3 2|
|2 3 a^2-1| = a^2-1 - 3 + 2 - 2(3-2) - 2(3-2) = a^2 - 4
D1 = |2 1 1|
|5 3 2|
|a+1 3 a^2-1| = 2(3(a^2-1)-6) - 1(5(a^2-1)-2(a+1)) + 1(15-3(a+1)) = 2(3a^2-9) - (5a^2-5-2a-2) + 12-3a = 6a^2 -18 - 5a^2 + 7 + 2a + 12 - 3a = a^2 - a + 1