During the Exam, if we have an identity matrix\begin{bmatrix}
1 & 0\\
0& 1
\end{bmatrix} do you want us to write out the matrix, write the abbreviation for it, or does it not matter?

For example, if you want to use $I$ for $2 \times 2$ matrix, then state that
“Let $I$ be the $2\times 2$ identity matrix.”
” We denote $I=\begin{bmatrix} 1 & 0\\ 0& 1 \end{bmatrix}$.”
Even though it is customary to use $I$ or $I_n$ for the $n \times n$ identity matrix, it is always good to explain what it means before you use it.