Math Help - Transition Matrix

I have a maths assignment and there is a question about transition matrices, and I'm finding it difficult because the teacher never taught us anything about them

The question is:
If Chuckie makes it to school on time he will make it on time the following day 85% of the time. However, if he doesn't make it on time, he will be late the next day 60% of the time.

i) Write down the transition matrix showing Chuckie's chances of getting or not getting to school on time.

ii) Chuckie was on time on Monday. What are the chances that he will be,
a) on time Wednesday?
b) on time Thursday?

iii) From this transition matrix determine the long term probability that Chuckie will make it to school on time.

If anyone could explain to me what a transition matrix is and how it works that would great Thanks!

It took me a moment to figure out that you were talking about a stochastic matrix/probability matrix (the more common names in my experience).

Anyways, Wikipedia has every little detail you could ever want to know about them, and Dr. Math some really good example problems that should make their practical use a lot clearer than the very general terms of the Wikipedia article.