I am uncertain regarding what this question is specifically asking?
"the columns of M form Michael's Basis, and the column Z form Zan's basis. If A is the matrix representation of transformation T in Michael's basis, what is the matrix representation of transformation T in Zan's basis"
I am assuming the name's Michael and Zan are distinct matrices. However, since I don't understand the relationship between the two matrices, Michael and Zan, as there appears to be none, would the solution just be A as well...It seems a bit trivial.
The matrix $M$ is the change-of-basis matrix from Michael's basis to the standard basis, whereas $Z$ is the change-of-basis from Zen's basis to the standard basis. Therefore, $Z^{-1}M$ is the change-of-basis matrix from Michael's basis to Zen's. So, the answer to your question is $$Z^{-1}MA(Z^{-1}M)^{-1}(=Z^{-1}MAM^{-1}Z).$$