Identity or Unit Matrix – Definition and Examples

Here you will learn what is the identity or unit matrix definition with examples.

Let’s begin –

Identity or Unit Matrix

Definition : A square matrix A = \([a_{ij}]_{n\times n}\) is called a identity or unit matrix if

(i) \(a_{ij}\) = 0 for all i \(\ne\) j and,

(ii) \(a_{ii}\) = 1, for all i

In other words, a diagonal matrix in which all the diagonal elements is unity is called the unit matrix.

The identity matrix of order n is denoted by \(I_n\).

Also Read : Different Types of Matrices – Definitions and Examples

Examples :

1). \(\begin{bmatrix} 1 & 0 & 0 \\ 0 &  1 & 0 \\ 0 & 0 &  1  \end{bmatrix}\) is a identity matrix.

The order of above matrix is \(3 \times 3\) and it is denoted by \(I_3\).

2). \(\begin{bmatrix} 1 & 0 \\ 0 &  1 \end{bmatrix}\) is a identity matrix.

The order of above matrix is \(2 \times 2\) and it is denoted by \(I_2\).

3). \(\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &  1 & 0 & 0 \\ 0 & 0 &  1 & 0 \\ 0 & 0 & 0 & 1  \end{bmatrix}\) is a identity matrix.

The order of above matrix is \(4 \times 4\) and it is denoted by \(I_4\).

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