Existence Nash Equilibria for zero-sum games

Question

I studied minimax theorem and I was wondering if it implies that every zero-sum game has a Nash equilibrium. I know that $\underset{x}{\max} \underset{y}{\min} x\cdot Ay= \underset{y}{\min}\underset{x}{\max} x\cdot Ay=v$ implies that $v=x^{*}\cdot Ay^{*}$, where ($x^{*}$,$y^{*}$) is a Nash equilibrium, is it true that every matrix A verifies show that every matrix $A$ verifies $\underset{x}{\max} \underset{y}{\min} x\cdot Ay= \underset{y}{\min}\underset{x}{\max} x\cdot Ay$, and hence it has a NE?