Square Matrix – Definition and Examples

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

Let’s begin –

Square Matrix

Definition : A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n.

A square matrix of order n is also called a n-rowed square matrix. The element \(a_{ij}\) of a square matrix A = \([a_{ij}]_{n\times n}\) for which i = j i.e. the elements \(a_{11}\), \(a_{22}\), …. , \(a_{nn}\) are called the diagonal elements and the line along which they lie is called the principal diagonal or leading diagonal of the matrix.

The order of a square matrix is \(n \times n\).

The general form of square matrix is \(\begin{bmatrix}a_{11} & a_{12} & …… & a_{1n} \\ a_{21} & a_{22} & …… & a_{2n}\\  . & . & . \\ a_{n1} & a_{n2} & …… & a_{nn}  \end{bmatrix}\)

Also Read : Different Types of Matrices – Definitions and Examples

Examples :

1). \(\begin{bmatrix} 2 & 1 & -1 \\ 3 &  -2 & 5 \\ 1 & 5 &  -3  \end{bmatrix}\) is a square matrix.

The order of above matrix is \(3 \times 3\) and diagonal elements are 2, -2 and -3.

2). \(\begin{bmatrix} 2 & 1 \\ 3 &  -2 \end{bmatrix}\) is a square matrix.

The order of above matrix is \(2 \times 2\) and diagonal elements are 2, -2.

3). \(\begin{bmatrix} 2 & 1 & -1 & 4 \\ 3 &  -2 & 5 & 1 \\ 1 & 5 &  -3 & 2 \\ 4 & 5 & 7 & 9  \end{bmatrix}\) is a square matrix.

The order of above matrix is \(4 \times 4\) and diagonal elements are 2, -2, -3 and 9.

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