# Scalar Matrix – Definition and Examples

Here you will learn what is the scalar matrix definition and order of scalar matrix with examples.

Let’s begin –

## Scalar Matrix

Definition : A square matrix A = $$[a_{ij}]_{n\times n}$$ is called a scalar matrix if

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

(ii) $$a_{ii}$$ = c, for all i, where c $$\ne$$ 0

In other words, a diagonal matrix in which all the diagonal elements are equal is called the scalar matrix.

## Examples :

1). $$\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$$ is a scalar matrix.

The order of above matrix is $$3 \times 3$$.

2). $$\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$$ is a scalar matrix.

The order of above matrix is $$2 \times 2$$

3). $$\begin{bmatrix} 3 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end{bmatrix}$$ is a scalar matrix.

The order of above matrix is $$4 \times 4$$.