MathDB

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, and
2. 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?

Problem Statement