(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T: M22→M22 be a LT defined by T(A)=AB where

B=[3,2

2,1]

Determine if T is invertible with respect to standard bases B=C={e11,e12,e21,e22}. If so, use (equation below) to find T^-1.

2. Relevant equations

[[T^-1 [AB]]_{C}= [T^-1]_{B to C matrix}[AB]_{B}(at least I think this is the right one)

3. The attempt at a solution

I found:

T= [ [3,2,0,0]’,[2,1,0,0]’,[0,0,3,2]’,[0,0,2,1]’ ]

T^-1 = [ [-1,2,0,0]’,[2,-3,0,0]’,[0,0,-1,2]’,[0,0,2,-3]’ ]

My TA told me I was doing this wrong and I can't figure out what to do. Can anyone help?

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# Homework Help: Inverse of the matrix of a linear transformation

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