Consider the system of equations A_{(n × n)} X_{(n × 1)} = λ_{(n × 1)} where, λ is a scalar. Let (λ_i, x_i) be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let $$I$$ be a (n × n) unit matrix. Which one of the following statement is NOT correct?

A. For a homogeneous n × n system of linear equations, (A - λ$$I$$)x = 0 having a nontrivial solution, the rank of (A - λ$$I$$) is less than n

B. For matrix A^m, m being a positive integer, (λ_i^m, x_i^m) will be the eigen-pair for all i

C. If A^T = A^-1, then |λ_i| = 1 for all i

D. If A^T = A, then λ_i is real for all i

Answer: Option B