Question 3 Which of the following are true for all invertible matrices A, B, C of the same size? Find a proof or counterexample in each case. -1 (a) (ABC) 1 A-¹B-¹C-1 -1 = (b) (ABA) = A-¹B-¹ A-1 -1 (c) (A¹) A = (d) −(-A)¯¹ = A−¹ (e) C-1 (ABC-1)−¹ AB = I -1 (f) (A+B)¹ = A−¹ + B−¹ (g) A¹(IA) A = A + I 1 (h) (AI) (A-¹-I) = A-¹ - A (i) A22A+ I = 0⇒ A¯¹ = 2I – A (j) A² - 2A+ I = 0⇒ A = I