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?

In general, when you use some notation for something, define it.

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.”

or

” 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.