Hello, MathIsRelativelyUseless!

I hope I understand the problem . . .

The matrix show the possible transitions from one state to anotherInitial transition matrix: .in one step.

The element in the upper-left, , represents

. . This says: the process cannotgo from state to state in one step.

The next element, represents

. . This says: the processcango from state to state in one step.

And so on . . .

If there is one intermediary computer, we are dealing with atwo-step process.

. . We want the matrix for all the possible two-step transitions.

This is a surprisingly simple process . . .

The two-step matrix is simply

. .

This can be read as another chart: .

The upper-left element, , representsin two steps.

. . The processcango from to in two steps (in two ways).

The next element, , represents in two steps.

. . The process cannotgo from to in two steps.

And so on . . .

And yes, for a three-step process, determine . . .