Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel?
(a) phi : R* maps to GL2(R) defined by
phi(a)= (1 0
0 a)
(b) phi :R maps to GL2(R) defined by
phi(a)= (1 0
a 1)
(c) phi :GL2(R) maps to R defined by
phi ((a b
c d)) = a+d
(d) phi : GL2(R) maps to R* defined by
phi ((a b
c d)) = ad-bc
(e) Phi: M2(R) maps to R defined by
phi ((a b
c d)) = b,
where M2(R) is the additive group of 2 x 2 matrices with entries in R.
