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7. Suppose A is an n x n invertible matrix and A is an eigenvalue of A. Suppose x is an eigenvector of corresponding

7. Suppose A is an n x n invertible matrix and A is an eigenvalue of A. Suppose x is an eigenvector of corresponding to A. (a) Show that A0, and x is an eigenvector of A-1 corresponding to eigenvalue A-. (b) Define a 2n x 2n matrix C and the vector y in R2" by A A-1 C= -] Is y an eigenvector of C? If yes, what is its corresponding eigenvalue?

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