Hi! Can you help me to find the solution of this problems? Thanks!

Given two points A=(0,0,1) and B=(1,0,1) in RP^2 (Projective space), consider the following lines:

a_1 : x+y-z=0
a_2 : x=0
a_3 : x-y+z=0

b_1 : x-z=0
b_2 : x-y-z=0
b_3 : y=0

1.Determine f:A --> B, which is the projectivity between the line pencil A and the line pencil B defined by the conditions f(a_i)=b_i. (A line pencil is the set of all lines passing through a given point)

2. By choosing appropriate bases for the pencils A and B, calculate the matrix fot f with respect to these bases.