Let A be an invertible matrix and A be an eigenvalue of A. Prove, using the definition of an eigenvalue, that is an eigenvalue of A-¹. (4) 11.2 If A is an invertible matrix that is diagonalisable, prove that A-1 is diagonalisable. (4) [8 marks] QUESTION 12 12.1 Let V and W be vector spaces and : VW be a linear transformation. For v EV, prove that T(-u) = -T(v). (3) 12.2 Let T: M₂2 M22 be defined by T(A) = A+AT. Show that T is a linear transformation. (0) [9 marks]