Which of the following function(s) define group homomorphisms?
I. f:GL2(R)→GL2(R) defined by f(A)=A2
II. f:Z4→Z defined by f(0)=0, f(1)=1, f(2)=2, f(3)=3
III. f:Z→Z4 defined by f(x)=x(mod4).
Notation:
GL2(R) is the group of invertible 2×2 matrices with real entries, with the operation being matrix multiplication.
Z is the additive group of the integers.
Z4 is the additive group of the integers modulo 4, whose elements are {0,1,2,3}.