Consider the system of linear equations A(n*n)X(n*1) = λ(n*1) where λ is a scalar. Let (λi , Xi) be an eigen pair of an eigen value and its corresponding eigen vector for a real matrix A. Let I be a n*n unit matrix. Which one of the following statements is not correct?
(A) for a homogeneous n*n system of linear equations (A-λI)X=0 having a non trivial solution, the rank of (A-λI) is less than n.
(B) for matrix A^m , m being a positive integer, ((λi)^m, (Xi)^m) will be the eigen pair for all i.
(C) if ( A's transpose= A's inverse ) , then mod(λi)=1 for all i.
(D) if (A's transpose = A) , then λi is real for all i