How To Find Inverse Of A Matrix

In the previous article, you learned about Inverse of Matrix and why it is important. We will explore how to find inverse of a matrix in this article. There are two primary method of finding inverse of any square invertible matrix – Classical adjoint method and Gauss -Jordan elimination method.

Methods To Find Inverse Of Matrix

The primary method of finding of inverse of matrix are

2. Gauss-Jordan elimination method

If $A$ is an invertible matrix then we can find the inverse of matrix $A$ with the adjoint of matrix $A$.

But,before we begin you must understand a few terminologies.

Determinant – It is a special number obtained from a Square Matrix, non-square matrix do not have determinants. If $A$ is a square matrix then there is a number of ways to denote its determinant.

$A = \begin{bmatrix}a & b\\c & d\end{bmatrix}$$det(A)$ or $\begin{vmatrix}A\end{vmatrix}$ or $\begin{vmatrix}a & b\\c & d\end{vmatrix}$$det(A)= ad - bc$

Minor of a matrix – The minor of a square matrix is determinant obtained by deleting a row and a column from the determinant of a larger square matrix. It is denoted by $M_{ij}$ for element $a_{ij}$ where $i$ is the ithrow and $j$ is the jth column.

The determinant of 2 x 2 matrix

$det(A) =\begin{vmatrix}a & b\\c & d\end{vmatrix}$$M_{11} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}d\end{vmatrix}$$M_{12} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}c\end{vmatrix}$$M_{21} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}b\end{vmatrix}$$M_{11} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}a\end{vmatrix}$

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How To Find Inverse Of A Matrix

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