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# Understanding a Square Matrix of Order 3

## What is a Square Matrix?

A square matrix is a matrix with the same number of rows and columns. This means that the number of elements in each row and in each column is the same. A square matrix of order 3 is a matrix with three columns and three rows.

## Examples of Square Matrices of Order 3

A few examples of square matrices of order 3 are given below.

$$\begin{bmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 6 & 7 \end{bmatrix}$$

$$\begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}$$

$$\begin{bmatrix} 10 & 11 & 12 \\ 13 & 14 & 15 \\ 16 & 17 & 18 \end{bmatrix}$$

## Properties of a Square Matrix of Order 3

The main properties of a square matrix of order 3 are given below.

• The number of elements in a square matrix of order 3 is 9.
• The sum of the elements in each row and in each column is the same.
• The sum of the elements in the main diagonal of the matrix is the same.
• The sum of the elements in the opposite diagonal of the matrix is the same.
• The trace of the matrix is the sum of the elements in the main diagonal.
• The determinant of the matrix is the product of the elements in the main diagonal.

## Conclusion

A square matrix of order 3 is a matrix with three columns and three rows. It has several properties, such as the sum of the elements in each row and in each column being the same, and the trace and determinant of the matrix being the sum and product of the elements in the main diagonal, respectively.

### References

https://www.mathsisfun.com/algebra/matrix-square.html