What is Square Matrix?
A square matrix is a type of matrix in mathematics where the number of rows is equal to the number of columns. This means that a square matrix has an equal number of elements along its horizontal and vertical dimensions.
The general form of a square matrix of order n is represented as follows:
[Tex]\mathbf{A} = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{bmatrix}[/Tex]
Determinant of a Square Matrix
Determinant of a square matrix is the scalar value or number calculated using the square matrix. The determinant of square matrix X is represented as |X| or det(X). In this article we will explore the determinant of square matrix in detail along with the determinant definition, determinant representation and determinant formula.
We will also discuss how to find determinant and solve some examples related to the determinant of a square matrix. Let’s start our learning on the topic “Determinant of a Square Matrix”.
Table of Content
- What is Square Matrix?
- What is Determinant of a Square Matrix?
- Determinant Representation
- Determinant Formula for 2×2 Square Matrix
- Determinant Formula for 3×3 Square Matrix
- How to Find Determinant for n × n Square Matrix
- Solved Examples
- Practice Questions
- FAQs