A) prove that if v is an eigenvector of a matrix a, then for any nonzero scalar c, cv is also an eigenvector of a. b) prove that if v is an eigenvector of a matrix a, then there is a unique scalar lambda such that av = lambda v. c) prove that a square matrix is invertible if and only if 0 is not an eigenvalue. d) prove that if lambda is an eigenvalue of an invertible matrix a, then lambda notequalto 0 and 1/lambda is an eigenvalue of a^-1. e) prove that if lambda is an eigenvalue of a matrix a, then loambda^2 is an eigenvalue of a^2.