Build Identity Matrix

Implement a function to generate an $n \times n$ identity matrix, a fundamental concept in linear algebra. The identity matrix is crucial in various mathematical operations, including matrix multiplication and transformation.

The identity matrix $I$ is defined such that when it multiplies another matrix $A$, the result is the original matrix $A$. This property makes the identity matrix the multiplicative identity for matrices. The elements of the identity matrix can be defined using the Kronecker delta $\delta_{ij}$, where $\delta_{ij} = 1$ if $i = j$ and $\delta_{ij} = 0$ otherwise.

To construct the identity matrix, follow these steps:

1. Initialize an $n \times n$ matrix with all elements set to 0.
2. Iterate over each row and column, setting the element at position $(i, j)$ to 1 if $i = j$, and 0 otherwise.

This technique is widely used in computer vision for image and signal processing.