First things first - multiplication of matrices is not necessarily commutative, and so does not in general imply that . It does, however, imply that .
I have a slight problem with the matrices you give - was the question "find the matrix " or "are and similar"? I ask this because I don't think they are similar. Trying to find a such that we discover that has determinant zero and so is non-invertible.
As a general rule for these questions, just hit them with a stick. What is ? What is ? just use a with variables for entries. All the entries must tally, and so what must look like? Even if you don't get the answer you will get some idea of what the matrix will look like, and so you can work from there.
There will often be more subtle methods, and these are worth looking out for. But the stick will always work...especially on 2x2 matrices!