Can you have a 2x2 magic square?

Can one truly possess a 2x2 magic square, or is this concept merely a mathematical illusion? By definition, a magic square requires the sums of its rows, columns, and often diagonals to be equal. Yet, given the constraints of a 2x2 grid, wouldn't this lead to a logical contradiction, as there would only be enough numbers to fill the square once, without allowing for the necessary manipulation to achieve the equal sums? Is it feasible, or is the quest for a 2x2 magic square a futile endeavor?