I have a few problems at which I'm at a loss. The first problem asks to "determine the elementary matrix that will multiply the third row of a 3x3 matrix by 2/3". I'm not even sure what this problem is asking. If A is a 3x3, is this problem asking for a matrix, B, which when you do AB, the third row of A is multplied by 2/3? The second problem says "Let lambda be an eigenvalue and v an associated eigenvector of matrix A. Prove that v is also an eigenvector for A^2. What is the associated eigenvlue?" I can't find anything about the properties of matrices and their powers? Might someone be able to offer a nudge or push in the right direction for either of these problems? Thank you.