Answer to Question #46067 in Linear Algebra for jasvinder

Question

Let T : R^2 -> R^2 and S: R^2 -> R^2 be linear operators defined by
T ( x(subscript1) , x(subscript2) ) = (x(subscript1) + x(subscript2) , x(subscript1) - x(subscript2)) and S( x(subscript1) , x(subscript2) ) = ( x(subscript1) , x(subscript1) + 2x(subscript2) )
respectively.
i) Find ToS and SoT.
ii) Let B ={ (1;0) , (0;1) } be the standard basis of R^3. Verify that
[ToS](subscriptB) = [T](subscriptB) o [S](subscriptB).