%-- 11/14/2014 2:30 PM --%
>> A = [1, -3; 1, 5]

A =

     1    -3
     1     5

>> X = [-3, -1; 1, 1]

X =

    -3    -1
     1     1

>> Xi = inv(X)

Xi =

   -0.5000   -0.5000
    0.5000    1.5000

>> Xi*A*X

ans =

    2.0000         0
    0.0000    4.0000