Help this is linear algebra question. I dont understand if i have to use the determinants to find the area. I find hard to understand the question i will appreciate if you explain it when youre doing it.

Consider a game between two players, Alice and Bob. In each round of the game, one of the two players will score a point. If one player scores a point, then the other player gets to go first in the next round of the game, and this increases their chances of scoring a point in the next round. When Alice and Bob play, then if Alice starts a round there is a 3/5 chance that she will score a point in that round. If Bob starts a round, there is a 1/2 chance that Bob will score a point in that round. Alice and Bob are about to play their game, and they have decided that Bob will play first. We know that, after round 1 of the game, there is a 1/2 chance that Bob will have scored, and a 1/2 chance that Alice will have scored. What is the probability that Bob scores a point in round 2, and what is the probability that Alice scores a point in round 2? Round 3? If the game of Alice and Bob goes on for a very long time, what is the probability that Bob scores a point in some very late round of the game, and what is the probability that Alice scores a point in some very late round of the game? (Hint: At each round of the game, we can write the probabilities that Alice or Bob will score a point that round as a 2-vector [8]. Given what was said in the first paragraph of the question, you should be able to write down a 2 x 2 transition matrix M, such that if our probabilities are [%] in some round of the game, then they will be M[6] in the next round. Once this is done, you can solve the three questions above by computing M and M2 and finding an equilibrium vector of probabilities p such that Mp=p.) [1/2] 1/2