# MDETERM

The `MDETERM` formula calculates the matrix determinant of a given square matrix. The determinant of a matrix is a scalar value that can be used to determine various properties of the matrix, such as whether it is invertible or singular.

## Usage

Use the `MDETERM` formula with the syntax shown below, it has 1 required parameter:

Parameters:
1. square_matrix (required):
The square matrix for which the determinant is to be calculated. The matrix should be entered as an array of arrays, where each sub-array represents a row of the matrix.

## Examples

Here are a few example use cases that explain how to use the `MDETERM` formula in Google Sheets.

### Determining Matrix Invertibility

By calculating the determinant of a matrix using the `MDETERM` formula, you can determine whether the matrix is invertible. If the determinant is non-zero, the matrix is invertible and has a unique inverse. If the determinant is zero, the matrix is singular and does not have a unique inverse.

### Solving Systems of Equations

The determinant of a matrix can be used to solve systems of linear equations. By using the `MDETERM` formula to calculate the determinant of the coefficient matrix, you can determine whether the system has a unique solution, no solution, or infinitely many solutions.

### Calculating Area and Volume

In geometry, the determinant of a matrix can be used to calculate the area of a parallelogram or the volume of a parallelepiped. By using the `MDETERM` formula to calculate the determinant of a matrix formed by the coordinates of the vertices of the parallelogram or parallelepiped, you can calculate its area or volume, respectively.

## Common Mistakes

`MDETERM` not working? Here are some common mistakes people make when using the `MDETERM` Google Sheets Formula:

### Incorrect matrix dimensions

The MDETERM formula can only be used on square matrices. If the matrix provided as input is not square (i.e. it does not have the same number of rows and columns), the formula will return an error. Make sure to provide a square matrix as input.

### Invalid input value

If any of the values in the input matrix are non-numeric, the MDETERM formula will return an error. Double-check that all values in the matrix are numeric.

### Missing input value

If any cell in the input matrix is empty, the MDETERM formula will return an error. Make sure all cells in the matrix have a value.

The following functions are similar to `MDETERM` or are often used with it in a formula:

• `MINVERSE`

The `MINVERSE` function in Google Sheets returns the inverse matrix of a given square matrix. The inverse matrix is such that when multiplied by the original matrix, it results in an identity matrix. This function is commonly used in linear algebra, such as solving systems of linear equations or finding determinants of matrices.

• `MMULT`

The `MMULT` formula in Google Sheets multiplies two matrices together and returns the resulting matrix. It is commonly used in linear algebra for matrix multiplication.

• `TRANSPOSE`

The `TRANSPOSE` formula in Google Sheets allows you to flip a table of data by turning rows into columns and columns into rows. This can be useful for reorganizing data or preparing it for use in other formulas.

You can learn more about the `MDETERM` Google Sheets function on Google Support.