Thread: i am so lost help me please

a) Let A and B be two 2 x 2 matrices, each of which commutes (multiplicatively) with C =
[ 0 1]. show that AB = BA
[ -1 0]

b) use mathematical induction to show that for all positive integers n,
[1 x y]^n
[0 1 x]
[0 0 1]
=
[1 nx ny+(n(n-1)/2)x²]
[0 1 nx]
[0 0 1]

i just started taking this class i have no idea where to start =(

a) Let A =
[a b]
[c d]

Given AC = CA perform the multiplications (AC and CA) and find out the relation between a,b,c,d for AC = CA to hold true . As BC = CB same relation will hold for elements of B. Under this relation you can show AB = BA

b) Again all you need to show is

[1 nx ny+(n(n-1)/2)x²]
[0 1 nx]
[0 0 1]

when multiplied by

[1 x y]
[0 1 x]
[0 0 1]

gives
[1 mx my+(m(m-1)/2)x²]
[0 1 mx]
[0 0 1]

where m=n+1