Here we look at the general idea of how to construct a transformation matrix, for use in quantum mechanics. A transformation matrix works to transform the state in some way, and there can be many different types of transformation operators, which makes them essential to understand. Here, I work through problem 1.26 from Sakurai, trying to provide ample thoughts and insights for the problem. This problem highlights a transformation matrix that transforms the Sz spin basis states to the Sx spin basis states.