Some involutory similarities

Matrices A,B over an arbitrary field F, when given to be similar to each other, are shown to be involutorily similar (over F) to each other (i.e.B = CAC^-1 for some C = C^-1 over F) in the following cases: (1)B= aI ? Afor some a ε F and (2) B = A^-1 . Result (2) for the cases where char F ≠ 2 is essentially a 1966 result of Wonenburger.