**A regular matrix of order n is a matrix that has the same number of rows and columns and its determinant is nonzero (0).**

In other words, a regular matrix of order n is a square matrix from which we can obtain the inverse matrix.

## Regular array formula

Given a matrix **V** with the same number of rows (n) and columns (m), that is, m = n, and with a non-zero determinant (0), then we say that **V** is a regular matrix of order n.

## App

The regular matrix is used as a label for the matrices that meet the conditions to have an inverse matrix.

- The matrix is a square matrix.

The number of rows (n) has to be the same as the number of columns (m). That is, the order of the matrix has to be n given that n = m.

- The matrix has a determinant and this is different from zero (0).

The determinant of the matrix must be nonzero (0) because it is used as the denominator in the inverse matrix formula.

## Theoretical example

Is matrix **D** a square and invertible matrix?

- We check if matrix
**D**meets the requirements to be a regular matrix.

- Is matrix
**D**a square matrix?

The number of columns in matrix **D** is different from the number of rows since there are 2 rows and 3 columns. Therefore, matrix **D** is not a square matrix, nor is it a regular matrix.

The first condition to be a regular matrix (square matrix condition) is a necessary and sufficient requirement since if it is not fulfilled it directly implies that the matrix is not a regular matrix and therefore we will not be able to calculate its determinant.

- Is matrix
**D**invertible?

Since matrix **D** is not square, we cannot calculate its determinant and decide if it is different from or equal to zero (0).

## Practical example

## Regular matrix of order 2

Is matrix **U** a square and invertible matrix?

- We check if matrix
**U**meets the requirements to be a regular matrix.

- Is matrix
**U**a square matrix?

The number of rows and the number of columns match in matrix **U.** So the matrix **U** is a square matrix of order 2.

- Is the matrix
**U**invertible?

First we will have to calculate the determinant of the matrix and then check that it is different from zero (0).

- Determinant of matrix
**U**:

- Check that the matrix
**U**is invertible:

So the matrix **U** is a regular matrix since it is a square and invertible matrix.

Inverse matrix of order 2