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,

[latex]A = \begin{bmatrix} a & b\\ c & d \end{bmatrix}[/latex]

The determinant of the matrix A is given by:

Det A = [latex]A=\begin{vmatrix} a & b\\ c & d \end{vmatrix}[/latex]

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.

Determinant Related Articles

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.

The determinant of a matrix of order one is the entry of the matrix. True or False?

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.

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