Question

What matrix 2x2 P1 projects the vector (x, y) onto the x axis to produce (x, 0)? What matrix P2 projecs onto the y axis to produce (0, y)?

Answer 1

Which gives a = 1, b=c=d=0.
You can do P_2 the same way, noting that P_2*(x,y) = (0,y)