Question 8 Let A be a square matrix with eigenvalue X. Prove the following implications. (a) A² = 0 λ = 0 (b) A² = A ⇒ λ = 0 or λ =1 (c) A² = I λ = 1 or λ = -1

For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.

Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.