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 \(I_4\).
