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# RD Sharma Class 12 Solutions Chapter 7 - Adjoint and Inverse of a Matrix (Ex 7.2) Exercise 7.2 ## RD Sharma Class 12 Solutions Chapter 7 - Adjoint and Inverse of a Matrix (Ex 7.2) Exercise 7.2 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 7 - Adjoint and Inverse of a Matrix Exercise 7.2 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 7 - Adjoint and Inverse of a Matrix Ex 7.2 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering Entrance Exams

Last updated date: 02nd Jun 2023
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## Adjoint And Inverse Of Matrix – Chapter 7, Mathematics (Class 12)

Chapter 7 of Mathematics in 12th grade is ‘Adjoint and Inverse of a Matrix’. Students will learn about Matrices which were also previously covered in the NCERT syllabus. The adjoint of a Matrix can be defined as the transpose of the cofactor Matrix of that particular Matrix.The Adjoint Matrix is also called the Adjugate Matrix. For a given matrix A, the adjoint is written as adj (A). In addition, the inverse of matrix A is that matrix that is multiplied by matrix A to give an identity matrix. The inverse of a matrix A can be denoted by A-1. This chapter will help students prepare for Engineering Entrances like IIT JEE (Prelims and Mains) as well as other state-based engineering entrance examinations. Students can get the help of subject experts to understand this lesson and also to clear their doubts if they have any.

### Some Of The General Tips For Effective Preparation.

1. Knowing the subjects and syllabus, make a day-wise timetable.

2. Dedicate a study area.

3. Fix a definite time for your studies.

4. Prepare your notes with all the formulas according to the chapter.

5. Note down difficult words, problems and theorems if any.

6. Revise every day.

7. Have proper sleep and healthy food.

9. Exercise regularly so both body and mind are full of energy.

10. Avoid studying for long hours continuously.

11. Take breaks in between so that you are always motivated.

## FAQs on RD Sharma Class 12 Solutions Chapter 7 - Adjoint and Inverse of a Matrix (Ex 7.2) Exercise 7.2

1. What are the properties of Inverse and Adjoint of a Matrix?

There are two properties of Inverse and Adjoint of a Matrix. The first one is for a square matrix A of order n, A adj(A) = adj(A) A = |A|I, where I am the identity matrix of order n. The 2nd property is that a square matrix A is invertible if and only if A is a non-singular matrix. These are the two properties of Inverse and Adjoint of a Matrix.

2. Can we do addition and subtraction in Matrices?

Yes, we can do several operations like addition, subtraction and multiplication if the Matrices are of the same dimension. Matrices can be defined by rows and columns. A common way to express Matrices is m x n or m by n where m is the number of rows and n is the number of columns. Thus, you may perform various operations if they satisfy the requisite conditions.

3. What are minors and cofactors?

Minor of an element aij of a determinant can be defined as the Determinant obtained by deleting its ith row and jth column in which element aij lies. Minor of an element aij is represented by Mij. Whereas, the cofactor of an element aij, denoted by Aij is defined by Aij = (–1) I + j Mij, where Mij is minor of aij. You must remember that if elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero.

4. Is this Chapter important for IIT JEE?

Yes, this Chapter is important for IIT JEE and other State Engineering Exams as well. The students might find it hard to cover the whole syllabus but the subject experts on Vedantu can help them, giving them proper guidance and the necessary tips required to complete the syllabus on time. It’ll be free of cost. Students can also register for IIT JEE coaching on Vedantu and start their preparations for the entrance examinations.

5. Can I get free NCERT solutions?

Yes, Vedantu provides free NCERT solutions which are solved with explanations. You can simply log in to the Vedantu app or website and find the necessary materials they are looking for. You can download the PDF file of the NCERT solutions which is free of cost and easy to refer to whenever it is required. In addition, you can talk to our subject-matter experts to clear your doubts if you have any. They have many years of teaching experience which will be extremely helpful for your studies.