Can I have some help with this

'5. {a} {1 point} State the denition of an eigenvalue. (h) {1 point) State the denition of an eigenspace. {c} {2 points} Prove that if A is an mm matrix satisfying that A\" is the zero matrix for some positive integer m, then the only eigenvalue of A is A = I]. (d) {3 points} Show that if A is a Self: matrix with exactly two distinct nonzero eigenvalues and the ran]: of A is 2, then A is diagonalizahle. {e} {3 points} Suppose that ALB are symmetric nxn matrices and Q is an orthogonal nxn matrix such that A = seer. B = @9201\". where D1 and g are diagonal matrices. If A and B are both negative denite. what is the deniteness of the symmetric matrix AB? Justify