This post explains how to calculate the determinant of a 1×1 matrix, also you will see several examples so that you do not have any doubt how to do it. Although this kind of determinants are very rare, the determinants of 1×1 dimension matrices are very easy to solve, as you will see below.
Table of Contents
What is a determinant of a 1×1 matrix?
A 1×1 determinant is a matrix of order 1, that is of a row and a column, represented with a vertical bar at each side of the matrix. For example, the following matrix has a single row and a single column:
Then, the determinant of matrix A is represented as follows:
As you have seen, writing the determinant of a square 1×1 matrix is very simple, since the matrix is formed only by 1 row and 1 column and, therefore, the determinant consists of a single number.
How to find the determinant of a 1×1 matrix?
Examples of determinants 1×1
Calculate the determinant of the following 1×1 matrix:
It is a 1×1 matrix, so the determinant of A is equal to the number that contains the matrix:
Find the determinant of the following 1×1 matrix:
It is a square matrix of order 1, so the determinant of B is:
Finding the determinant of a 1×1 matrix is not complicated, but you have to pay attention to the sign of the number.
Do not confuse the determinant of a 1×1 matrix with the absolute value of a number.
The result of a 1×1 determinant is always equal to the value of the matrix, regardless of the sign
Instead, the absolute value transforms the number inside the operator into positive