# Determinant of a Matrix of Order One

Determinant of a matrix of order one is equal to the entity or element that is present in the matrix. A determinant is the value associated with the square matrix of order m. It is denoted by Det (A) or |A|, where A is a matrix.

Facts:

• Only a square matrix can have a determinant
• A determinant can be a real or complex number
• The determinant of the matrix of the order m x n, where m is not equal to n, cannot be determined

## Determinant of 1 x 1 Matrix

For square matrix say,

$A = \begin{bmatrix} a & b\\ c & d \end{bmatrix}$

The determinant of the matrix A is given by:

Det A = $A=\begin{vmatrix} a & b\\ c & d \end{vmatrix}$

Det A = ad – bc

Now, if A is a matrix of the order 1 x 1, such that;

A = [a]1×1

Then, the determinant of matrix A is given by;

Det (A) = a

Or

|A| = a

Note: |A| does not express the modulus of A here, but the determinant of A.

### Examples of Determinant of Order One Matrices

1. The determinant of matrix A = [2]1×1 is:

Det A = 2

2. The determinant of matrix B = [-1]1,1 is:

|B| = -1

3. The determinant of the matrix of order one, A = [100]1×1 is:

Det A = 100

4. The determinant of matrix A with order 1 x 2 cannot be determined.

## Frequently Asked Questions on Determinants of Matrix of Order One

### What is the determinant of the matrix of order one?

The determinant of the matrix of order one, is equal to the single element present inside the matrix. If matrix A = [a], then the determinant of A is a.

### What is the symbol of determinant?

The determinant of a matrix A is denoted by det(A) or |A|.

### How to find the determinant of a 3 x 1 matrix?

The determinant of the 3 x 1 matrix cannot be determined.

True

### What is the product of two 1×1 matrices?

When a 1 x 1 matrix is multiplied by another 1 x 1 matrix, then the resulting matrix is also of the same order, i.e.1 x 1.