Matching Pennies is Strictly Competitive

Theorem
The game of Matching Pennies is strictly competitive.

Proof
By definition, a strictly competitive game is a game in which the interests of each player are diametrically opposed.

Recall the payoff table of Matching Pennies:

It can be seen by inspection that exchanging $\text A$ and $\text B$ results in exactly the same entries in the payoff table.

From the nature of a payoff table it follows that the fortunes of each player are opposite and equal.

Hence the result.