FINDING INVERSE OF A MATRIX USING FORMULA

What is inverse of a matrix ?

For a square matrix A, the inverse is written A-1When A is multiplied by A-1 the result is the identity matrix I. Non square matrices do not have inverses.

Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called non invertiable or singular.

Formula to find the inverse of the matrix :

Example 1 :

Find the inverse of the following matrix

 
2 1 1
1 1 1
1 -1 2
 


Solution :

|A|  =  2(2+1) - 1(2-1) + 1(-1-1)

|A|  =  2(3) - 1(1) + 1(-2)

|A|  =  6-1-2

|A|  =  3  ≠ 0

Since A is a non singular matrix. A-1 exists.

Example 2 :

Find the inverse of the following matrix

 
1 2 1
2 -1 2
1 1 -2
 


Solution :

|A|  =  1(2-2)-2(-4-2)+1(2+1)

  =  1(0) - 2(-6)+1(3)

  =  12 + 3

|A|  =  15  ≠ 0

Since A is a non singular matrix. A-1 exists.

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