Compute the inverse of the matrix 1 1 0 a 1 0 0 1 1 for all

Compute the inverse of the matrix [1 1 0 a 1 0 0 1 1] for all a for which it exists. For which a elementof R does the inverse not exist?

Solution

determinant = 1(1*1 - 0*1) -a (1*1 - 0*1) + 0
= 1-a

for inverse to exist, determinant must not equal = 0
so,
1-a !=0
a!=1

so,
a= R -{1}

a can be anything except 1