Let A be and B be n x n matrices, assume that is an eigenvector of the matrix product AB. Assume that Bx ‡ 0. Prove that Bx is an eigenvector of BA.

Please show all work when completing this proof

Let A be a 3x3 symmetric matrix. Assume that A has two eigenvalues: A₁ = 0, and X₂ X2 independent eigenvectors of A corresponding to X₁: 1 H 1 1 Find a non-zero vector V3 which is an eigenvector of A corresponding to A₂. Enter the vector V3 in the form [C₁, C₂, C3]: V₁ = 9 V₂ = 2 2 0 2. The vectors V₁ and V₂ given below are linearly

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