1. The problem statement, all variables and given/known data T: M22 --> M22 defined by T(A) = AB where B = [ 3 2 ] [ 2 1 ] Is the linear transformation matrix T invertible with respect to the standard bases? If so, find it. 2. Relevant equations none 3. The attempt at a solution This is going to sound stupid, but I need help in finding what the transformation matrix T actually is before I can say if it is invertible or not. So far I got: T(A) = AB = [a b ] [ 3 2 ] [c d ] [ 2 1 ] = [ 3a+2b 2a+b ] [ 3c+2d 2c+d ] and I found T(e11) = [3 2 ] [0 0 ] T(e12) = [ 2 1 ] [ 0 0 ] T(e21) = [ 0 0 ] [ 3 2 ] T(e22) = [ 0 0 ] [ 2 1 ] and now I'm stuck. Thinking ahead a little, I know that if the kernal of T = 0, it will be invertible, or if the determinant of the matrix is not 0, it is invertible. P.S. is there an easier way to write matrices here?