8. Our method of drawing arrows to look for Nash equilibria becomes too messy in a 3x3 or larger payoff matrix. Instead we'll just examine each possible answer.

TL, BR TL is a Nash equilbirium because neither player would wish to change unilaterally. Without changing, Player 1 earns a payoff of 4. The only alternatives are that she could choose M for a payoff of 2 or B for a payoff of 1. Player 2 gets a payoff of 7 by staying with L, C and R earn payoffs of 2 and 4, both lower. BR is also a Nash equilibrium. Player 1 gets 9, her other choices only payoff 5 or 6. Player 2 gets 10, her only choices are 8 and 9.
MC, MR From MC Player 2 would like to switch to R if Player 1 were going to play M so this isn't a Nash equilibirum. At MR Player 1 would like to switch to B if Player 2 were going to stay at R so this too isn't a Nash Equilibrium.
ML, BC From ML, Player 1 would switch to T (if Player 2 would stay put at L) and Player 2 would switch to R (if Player 1 would stay put at M). If either player would switch this can't be a Nash equilibrum. From BC Player 1 would switch to M (if Player 2 would stay put at C) and Player 2 would switch to R (if Player 1 would stay put at B)
TR From TR Player 1 would switch to B (if Player 2 would stay put at R) or Player 2 would switch to L (if Player 1 would stay put at T)
There are no pure strategy equilibria. We've shown this to be wrong since there are two given in answer (a).