G=2x2 matrixes with a1a1=m, a1a2=b, a2a1=0, a2a2=1. (where integers are viewed as residue classes in Z/5Z)
H=2x2 matrixes with a1a1=1, a1a2=c, a2a1=0, a2a2=1.
Prove that the quotient/factor group G/H is cyclic and of order 4.
I'm confused because I can't see how its of order 4. I think its should be 5. Any help is appreciated!!