An identity matrix is a square matrix where all the elements on the main diagonal are $1$s and all other elements are $0$s. It is denoted by $I_n$, where $n$ is the dimension of the matrix. For example, the $2 \times 2$ identity matrix is: $$ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$ And the $3 \times 3$ identity matrix is: $$ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ The final answer is $\boxed{\text{An identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere.}}$