Answer
False
Work Step by Step
We will analyse the matrix $A=I_2$ with the determinant:
$\det(A)=1$
When each element of an $m×n$ matrix is doubled, which is $2A$, the determinant will be:
$\det(2A)=\det \begin{equation*}
B =
\begin{bmatrix}
2 & 0\\
0& 2\\
\end{bmatrix}
\end{equation*}=4$
$\frac{\det(A)}{\det(2A)}=\frac{1}{4}$
Hence, statement "each element of an $m×n$ matrix is doubled, then the determinant of the matrix also doubles" is false.
