IMC 2023 Problem 6

Ivan writes the matrix $\begin{pmatrix} 2 & 3 2 & 4\end{pmatrix}$ on the board. Then he performs the following operation on the matrix several times:1. he chooses a row or column of the matrix, and2. he multiplies or divides the chosen row or column entry-wise by the other row or column, respectively.

Can Ivan end up with the matrix $\begin{pmatrix} 2 & 4 2 & 3\end{pmatrix}$ after finitely many steps?