Question

In this textbook of "Introduction to Linear Algebra" by Prof. Strang, Problem 17 in Problem Set 4.2 says When P projects onto the C(A), I-P projects onto the left kernel of A!!
I understood that P = Ax is in C(A) but It's complicated to me to use I-P instead of P.
What effects did Identity on "I-P projects onto the N(A Transpose)?
Is there anyone explain it for me? I'm gonna die!!!

Answer 1

e=b-p is the left null space , or I-P both are the same and both are orthogonal on the C(A)