Introduction

In the field of linear algebra, the identity matrix plays a pivotal role. It is a square matrix with ones on the main diagonal and zeroes everywhere else. This post will discuss how to determine whether a given square matrix is an identity matrix.

Applications

Identity Matrix Definition

An identity matrix is a square matrix where all elements in the main diagonal are ones and all other elements are zeros. It is denoted by I or I_n for an n x n matrix. The identity matrix is the multiplicative identity in the set of all square matrices.

Checking for Identity Matrix

To determine if a matrix is an identity matrix, one needs to confirm that all elements on the main diagonal are one and all other elements are zero. More formally, a matrix A is an identity matrix if and only if A[i][j] = 1 for all i = j and A[i][j] = 0 for all i ≠ j.

References

• Identity Matrix - Wikipedia
• Identity Matrix - MathWorld