If the number of rows and number of columns of a matrix are equal, then the matrix is said to be a

Square matrix. A =

$\left [a_{i,j} \right ]_{m\times m }$** **is a square matrix of order mxm.

The elements $a_{ij}$ of a square matrix for which i = j

* *are called as Diagonal elements and the line along which they lie is said to be the Principal Diagonal of the given matrix. Let us look at few examples below:

In the above examples, 2, 8 are the diagonal elements of the matrix A and -1, 3, 1 are the diagonal elements of matrix B. The highlighted lines of matrices A and B are the Principal Diagonals.

### Square Matrix Examples

$A_{2\times 2}$=$\begin{bmatrix}

a &b \\

c &d

\end{bmatrix}$ is a square matrix of order 2x2.

$B_{3 \times 3}$ =$\begin{bmatrix}

b_{11} &b_{12} &b_{13} \\

b_{21} &b_{22} &b_{23} \\

b_{31} &b_{32} &b_{33}

\end{bmatrix}$ is a square matrix of order 3x3.

$C_{4 \times4}$=$\begin{bmatrix}

1 &3 &-5 &7 \\

2 &4 &6 &-8 \\

3 &3 &9 &0 \\

0 &3 &4 & 1

\end{bmatrix}$ is a matrix of order 4x4.