Thread: Lie Group homomorphism questions.

URGENT - Please help with the below questions:
(presentation tomorrow)

1. If G1 & G2 are matrix groups and F is a Lie Group isomorphism: F: G1 -> G2 then the differential dF: L(G1) -> L(G2) is also an Isomorphism.

2. Suppose G1, G2, G3 are Lie (matrix) groups and
F1: G1 -> G2
F2: G2 -> G3
are Lie group homomorphism. dF1 and dF2 are linear transformation such that:
dF1: L(G1) -> L(G2)
dF2: L(G2) -> L(G3)
show that: d(F2 o F1) = dF2 o dF1

Thanks guys!