(a) Show that if is an eigenvalue of A then k is an eigenvalue of Ak (b) What is wrong with this proof generalizing that If is an eigenvalue of A and is an eigenvalue for B, then is an eigenvalue for AB, for, if Ax x and Bx x then ABx Ax Ax x

Question: (a) Show that if is an eigenvalue of A then k is an eigenvalue of Ak. (b) What is wrong with this proof generalizing

(a) Show that if λ is an eigenvalue of A then λk is an eigenvalue of Ak.
(b) What is wrong with this proof generalizing that? "If λ is an eigenvalue of A and λ is an eigenvalue for B, then λμ is an eigenvalue for AB, for, if A→x = λ→x and B→x = λ→x then AB→x = Aλ→x = λA→x λ→x"?

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