# #f:M_2(RR)->M_2(RR);f(X)=AXA^(-1);A inM_2(RR);A-#inversable;How to demonstrate that #f# is an bijective function?

##### 1 Answer

Apr 3, 2017

#### Explanation:

Note that if we define:

#g(X) = A^(-1)XA#

then:

#g(f(X)) = A^(-1)(f(X))A = A^(-1)AXA^(-1)A = IXI = X#

#f(g(X)) = A(g(X))A^(-1) = A A^(-1)XA A^(-1) = IXI = X#

So

The domains of