The determinant in mathematics helps us find an inverse of a matrix. The determinant of a matrix is a number that is specifically defined only for square matrices. The determinant is used in many instances in calculus and other matrix-related algebra; it actually serves the matrix in terms of a real number which can be used in solving the system of linear equations and finding an inverse of a matrix.

**det in R**

To calculate the determinant of a matrix in R, use the det() function. The det() is a built-in R generic function that returns the determinant’s modulus separately, optionally on the logarithm scale and the determinant sign. The set() function takes data as required and logarithm as an optional argument and returns the determinant, never the determinant’s logarithm.

**Syntax**

`det(data, logarithm = TRUE, ...)`

**Parameters**

**data**: It is a matrix whose determinant we need to calculate.

**Logarithm**: It is a logical argument; If **TRUE** (default) returns the logarithm of the determinant’s modulus.

**…: **These are the further arguments passed to or from other methods.

**Example**

To create a matrix in R, use the **matrix() **function. The dimension of the Matrix is defined by **nrow **and **ncol **property.

```
vt <- c(-1, -3, -5, -7, -8, 9, 11, 13, 15)
mtrx <- matrix(vt, nrow = 3, ncol = 3)
print(det(mtrx))
```

**Output**

```
[,1] [,2] [,3]
[1,] -1 -7 11
[2,] -3 -8 13
[3,] -5 9 15
```

Now, let’s find the determinant of the matrix using the **det()** function.

```
vt <- c(-1, -3, -5, -7, -8, 9, 11, 13, 15)
mtrx <- matrix(vt, nrow = 3, ncol = 3)
print(det(mtrx))
```

**Output**

`[1] -360`

The determinant of the above matrix is -360. Now, if you transpose the matrix and then calculate the determinant, then also it will return the same output as above. Let’s see how to do that.

The **Transpose of a Matrix** is defined as “A **Matrix** which is formed by turning all the rows of a given **matrix** into columns and vice-versa.”

To transpose a matrix in R, use the **t()** method.

```
vt <- c(-1, -3, -5, -7, -8, 9, 11, 13, 15)
mtrx <- matrix(vt, nrow = 3, ncol = 3)
t_m <- t(mtrx)
print(t_m)
```

**Output**

```
[,1] [,2] [,3]
[1,] -1 -3 -5
[2,] -7 -8 9
[3,] 11 13 15
```

Okay, now let’s find the determinant of this transposed matrix.

```
vt <- c(-1, -3, -5, -7, -8, 9, 11, 13, 15)
mtrx <- matrix(vt, nrow = 3, ncol = 3)
t_m <- t(mtrx)
print(det(t_m))
```

**Output**

`[1] -360`

That is it for det() function in R.

**See also**

Krunal Lathiya is an Information Technology Engineer by education and web developer by profession. He has worked with many back-end platforms, including Node.js, PHP, and Python. In addition, Krunal has excellent knowledge of Data Science and Machine Learning, and he is an expert in R Language. Krunal has written many programming blogs, which showcases his vast expertise in this field.