im trying to prove that 0 is an eigenvalue of A iff A is non invertible. may i know why for a homogeneous solution Ax = 0 to have a non trivial solution, it means that A in non-invertible?

cant it be that x is a zero vector?

if det of A is non-zere, where A is invertible, then there doesnt exist a non trivial solution in the homogenous solution Ax=0?

i think im confusing myself:/

thanks.