I was using the wrong matlab function for matrix inverse.
I got this output for 2b)
A =
-0.7000 0.2000 0.5000 0 0
0.3000 -0.3000 0 0 0
0.3000 0.5000 -1.0000 0.2000 0
0 0.7000 0 -1.0000 0
0.3000 0.5000 0.2000 0 -1.0000
B =
-1
-1
-1
-1
-1
>> A\B
ans =
111.1111
114.4444
107.7778
81.1111
113.1111
these are answers to muA, muNotA, muAG, muAGG, muAGGA. Notice we had to set muAGGA to 0 in the 4th row because expected wait time to get to AGGA when you transition to AGGA should be 0.