Adjoint and Inverse of a matrix - meaning, abbreviation and method

Adjoint of a matrix is the transpose of a square cofactor matrix.
If the matrix is named A, the adjoint of the matrix will be denoted as 'Adjoint A' or 'Adj A'.

Method;

For a clear understanding about the adjoint of a matrix let’s consider a 2*2 matrix; the following 3 steps are to be followed:

Step 1: We to find the cofactor of each element.
If in case you don't know how to find the cofactor of a matrix;
https://basicmathematix.blogspot.in/2018/04/co-factors-of-matrix-and-cramers-rule.html

Step 2: We find the transpose of the cofactor matrix.
It means that we interchange the rows and columns of the cofactor matrix which we have obtained in step 1.

Inverse of a matrix is it's adjoint divided by the matrix's determinant.
Inverse of a matrix is denoted as "A^−1".

Method;
Step 1: We have to find the determinant of the matrix.
If in case you don't know how to find the determinant of a matrix;
https://basicmathematix.blogspot.in/2018/04/transpose-of-matrix-matrixs-determinant.html
Step 2: We have to find the adjoint of the matrix. The method is described above.
Step 3: We have to divide the adjoint of the matrix(as obtained in step 2) and divide it with the matrix's determinant(as obtained in step 1)
So in the end these steps can be understood in one single formula;