Can I get some help with this assignment question? I need the answer by 4 PM. Thank you.

1. assume that the matrix X is idempotent.

a) give two examples of 2x2 matrices which are idempotent matrices and which all entires are non-zeros

b) prove that I - X is also Idempotent matrix. what is X(I -X) equal to?

c)Prove that for any square matrix A of the same size as X, the Matrix Y= X+ AX - XAX is also idempotent matrix

d) assuming now that X is also invertible, prove that X=I