>>776
Yep, it exists. For \( X=A \cdot B \) with A,B \( n \cdot n \) matrices  \( \neq I_n \)
because the product between matrices isn't commutative.
So \( X \cdot Y-Y \cdot X = A \cdot B \cdot Y - Y \cdot A \cdot B = I_n)