Question

@ if A^-1(inverted) matrix exists and B matrix and S matrix prove these AB=BA and S^2 =B prove that (A^-1SA)^2=B

Answer 1

1. A is invertible
2. AB = BA
3. S^2 = B

Show that \( (A^{-1}SA)^2 = B \).

So just start calculating:
\[ (A^{-1}SA)^2 = A^{-1}SAA^{-1}SA = ... \]

Answer 2

nice translation of the question ... :)

Answer 3

Thanks. ;-) I guess I shouldn't be surprised, but it is interesting how often clarifying the question to "well posed" is necessary on here.

Answer 4

so in the end it is ...=I*B am I right ?

Answer 5

and IB = B, by definition of I