Let A be a 2 x 2 matrix such that A = 2, 3 are eigenvalues for A. Assume that () and are eigenvectors of 2 and 3 respectively. Find the matrix A.

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are - 10, 2, and - 2. - 4 - 4 - 2 A = - 4 -2 - 4 2 -4 - 4 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)

For matrix A, find the associated eigenvalues. A = [] O2 and 3 O3 and 5 O1 and 5 5 and -1

Let A and B be nxn matrices. Show that if A is an eigenvalue of AB, then A is also an eigenvalue of BA.