How to Find Determinant for n × n Square Matrix
To find the determinant for n × n square matrix we follow following steps:
- First, select any row or column of the given matrix.
- Then, for each element aij in the selected row find its cofactor Cij.
- The cofactor of aij is given by: Cij = (-1)i + j Mij where Mij is minor of aij
- The minor of aij is the determinant obtained by eliminating ith row and jth column in the matrix.
- After finding all the cofactors of selected row/column element multiply each element with its cofactor and add them.
- The resultant gives the determinant of the given n × n square matrix.
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