Which one of the following statements is TRUE about every n × n matrix with only real eigen values?

A. If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigen values is negative

B. If the trace of the matrix is positive, all its eigen values are positive

C. If the determinant of the matrix is positive, all its eigen values are positive

D. If the product of the trace and determinant of the matrix is positive, all its eigen values are positive

Answer: Option A