Did you read my tips on how to study and learn Math 1300?  If not, here is a link to those important suggestions:

Did you see my tips for Assignment 1? Click here.

Did you see my tips for Assignment 2? Click here.

Did you see my tips for Assignment 3? Click here.

Here is a link to the actual assignment, in case you don't have it handy:

Study Lesson 3 (Matrix Math), Lesson 4 (The Inverse of a Matrix and Applications), Lesson 5 (Elementary Matrices), and Lesson 14 (Markov Analysis) from my Linear Algebra & Vector Geometry book to prepare for this assignment.

This is just classic matrix math stuff as taught in Lesson 3 of my book.

Look at my Lesson 3, question 4 and Practise Problem 31 for some strategies to employ here.

You know B is invertible, so work B-inverse into the equation you were given.

Classic inverse matrix stuff as taught in Lesson 4 of my book.  Note that you can verify that your answer is correct by confirming that the product of A and A-inverse is the Identity matrix.

This is just classic elementary matrix stuff as taught in Lesson 5 of my book.  Question 5 is especially similar.

Remember what I told you about diagonal matrices in Lesson 3.  I also gave you a shortcut to find the inverse of a 2 by 2 matrix in that lesson, too.

Hint: Since A=PDP-inverse, then A-squared would be (PDP-inverse)-squared = PDP-inverse*PDP-inverse.  How does that simplify?  What if it were A^3? A^4? A^2016.

This is a Markov Analysis question similar to my questions in Lesson 14. 

When you are finding the steady-state or stable vector, don't worry about the little tricks I use.  Set up the augmented matrix with a row of ones all the way through the first row, then the rest of the augmented matrix is I - T for the coefficients augmented with a column of zeros.  In other words, do Step 1 as I outline at the start of Lesson 14.  At that point, merely row-reduce the way you always do.  Don't worry about the fancy tricks I show about making zero rows and stuff.  Row-reduce like usual, and the system will solve itself.  I really regret over-complicating this lesson by giving too many tricks when it is ultimately just a row-reduction problem. 

DO NOT USE THE CRAMER'S RULE METHOD I DEMONSTRATE!  Obviously, since that isn't even taught until later in the course (Lesson 8 in my book).  Even after you do learn Lesson 8, do not use this approach to solve Markov.  Unnecessary.  Stick to good old row-reduction.