Weakly dominance in Zero Sum game

Question

With the following game matrix in Zero sum games:

  a  b     
A -1  2 

As b dominates over a - does this still prove there is Nash Equilibrium using minimax theorem ?

Answer 1

According to usual interpretation, Column minimizes so actually $a$ dominates $b$. Regardless, the minimax outcome for this game (following the usual interpretation) is $(A,a)$.