Identity Matrix

Topics: Algebra

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An identity matrix $I$, also called an $n\times n$ identity matrix and denoted by $I_n$, is a matrix that takes the form:

$$I_1=\left(\begin{array}{c}1\end{array}\right)$$

$$I_2=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$$

$$I_3=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$$

$$I_n=\left(\begin{array}{ccccc}1& 0& 0& \cdots & 0\\ 0& 1& 0& \cdots & 0\\ 0& 0& 1& \cdots & 0\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ 0& 0& 0& \cdots & 1\end{array}\right)$$

These matrices serve as the multiplicative identity element when multiplying the respective $n\times n$ matrices.