Show that is an eigenvalue of Alf and only if is an eigenvalue of A. Hint: Find out how A-land Al - are related. In order for to be an eigenvalue of Aand A', there must exist nonzero x and such that and -AL. Use matrix algebra and the equations from the first step to write matrix equations involving A-land A The equations are and Matrix A- m atrix A-1. How can this relationship between A-land A-l be used to determine information about? O A Since the two matrices are equal, the nonzero vectors x and must also be equal OB. Since the two matrices are transpotes, Weither A x or ( A I) has at least one notrivial solution, then all of the statements of the invertible Matrix Theore are false for both matrices OC. Since the two matrices are equal, the norwero vector must be a constant multiple of the nonzero vector v OD. Since the two matrices are inverses, If either ( A x or (A-AT) has at least one notrivial solution, then all of the statements of the invertible Matrix Theorem true for both matrices Why does this show that is an eigenvalue of Art and only it is an eigenvalue of A? OA X is an eigenvalue of either of A then it is an eigenvalue of both A and A' because if a nonzero vector xor exists, then the other must also exist because of the relationship between them. US is eigenvalue of the Aor Al, then it is an eigenvalue of both A and A' because both matrices A-land A a re invertble. s eigenvalue of the Aor Althen it is an eigenvalue of both A and A' because both (Al-Ix and ( A I) have at least one notrivial solution OD is an eigenvalue of either ArAthen it is an eigenvalue of both A and A because A and A are transposes and A-land A-l are transposes. O