In linear algebra, the identity matrix of size $$n$$ is the $$n \times n$$ Square matrix with ones on the main diagonal and zeros elsewhere.

$$\href{/posts/identity_matrix}{I_{1}}=\begin{bmatrix}1\end{bmatrix}, \; \href{/posts/identity_matrix}{I_{2}}=\begin{bmatrix}1&0\\0&1\end{bmatrix}, \; \href{/posts/identity_matrix}{I_{3}}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}, \; \dots , \; \href{/posts/identity_matrix}{I_{n}}=\begin{bmatrix}1&0&0&\cdots &0\\0&1&0&\cdots &0\\0&0&1&\cdots &0\\ \vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\cdots &1\end{bmatrix}.$$