# Find the inverse

Let the given matrix we have to find A-1.

Now A-1 will exist only of |A| ≠ 0

Let us first find |A|

|A| = (-3) (-3) – (5)(2)

|A| = 9 – 10 = -1

Hence |A| ≠ 0 and A-1 exist

Now A-1 is given by

Now adjoint(A) = CT where C is the cofactor matrix and CT is the transpose of cofactor matrix

The cofactor is given by

Cij = (-1) i+jMij …(a)

Where M represents minor

Mij is the determinant of matrix leaving the ith row and jth column

The cofactor matrix C will be

Now transpose of C that is CT

For CT we will interchange the rows and columns

Using (a)

From matrix A the minors are

M11 = -3, M12 = 5, M21 = 2 and M22 = -3

Now inverse of A is

Now we have to solve the matrix equation

As we know that AA-1 = I hence multiply equation by A-1 from right side where I is identity matrix

Hence

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

Using matrices soMathematics - Board Papers

On her birthday SMathematics - Board Papers

Using matrices soMathematics - Board Papers

<span lang="EN-USRS Aggarwal - Mathematics

<span lang="EN-USRS Aggarwal - Mathematics

Using elementary RS Aggarwal - Mathematics

Using elementary RS Aggarwal - Mathematics