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1. (OC 16) Assume that A is an n x n invertible matrix with eigenvalue 3. (a) Find an eigenvalue for A2. Justify your answer. b) Find an eigenvalue for A~1. Justify your answer. g Yy 2. (OC 16) Assume that A and B are n x n matrices and that the vector x is an eigenvector for each of them. Assume that A4 is the associated eigenvalue for the matrix A and Ap is the associated eigenvalue for the matrix B. Show that AgAj4 is an eigenvalue for AB and BA. 3. (OC 16) The 4 x 4 matrix A is such that the first two columns of A? are identical. Show that zero must be an eigenvalue of A