The number of different non-singular matrices of the type A=1ac11b0−ww  where w=eiθ  and a,b,c∈{z:z4−1=0}  are

|A|=w(1+b−a−c)For non singular matrices |A|≠0Total number of different matrices of type A=43=64No. of singular matrices : |A|=0⇒1+b=a+cThere are only 9 possible cases.So only 9 matrices are singular ⇒  No of non–singular matrices = 64 – 9 = 55