# RD Sharma Class 12 Chapter 7 Solutions (Adjoint And Inverse Of A Matrix)

RD Sharma Class 12 Maths Solutions for Chapter 7 can resolve all the queries that arise while you prepare for your Maths exams. In this chapter, you will learn about the Matrix in a comprehensive way. The topics you will come across in this chapter are definitions, the inverse of a matrix, useful results on the invertible matrices, determining adjoints and the inverse of a matrix and most importantly when it satisfies the matrix equation, finding non-singular matrices when the adjoint is given, finding the inverse using the definition of an inverse, etc. You will also learn about the elementary transformation and the method of finding the inverse by the elementary transformation.

Adjoint and Inverse of a Matrix contains 2 exercises in total. The solutions to all the chapter-end questions will be provided to you too in a detailed and step by step format to ensure for your best learning experience. Our subject matter experts have ensured that solutions are in compliance with your CBSE guidelines. The solutions are structured in a way that will help you well for a better understanding of this chapter.

## Summary of RD Sharma Class 12 Maths Solutions Chapter 7 – Adjoint and Inverse of a Matrix

The RD Sharma Solutions Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix will introduce you to a diverse range of topics. It is also going to teach you practical applications of the Adjoint and Inverse of a Matrix. Here are some topics you will come across in this chapter:

**Definition of an Adjoint of a Matrix**

In this topic, you will learn about the definition of an Adjoint of a Matrix. It is defined as the transpose of the Matrix. The Adjoint of Matrix B is denoted by Adj B and so on.

**Finding the Inverse of a Matrix**

In this portion, you will be taught about how to find the inverse of a matrix. In order to find the inverse of a matrix, it is important to first define the matrix. It is important to note that an inverse is defined only by non-singular matrices. The below explanation determines the relationship between a matrix and its inverse:

AA-1 = A-1A = I, where I is the identity matrix.

**Theorems Related to Adjoint and Inverse of a Matrix**

Here, you will be introduced to the four theorems on Adjoint and Inverse of a Matrix. Ensure to revise all four theorems thoroughly with their individual proofs.

Theorem 1: This theorem says that If A is a given square matrix of order n, then A adj(A) = adj(A) A = |A|I, where I is the identity matrix of order n.

Theorem 2: This theorem states that if both A and B are matrices that are non-singular of the same order, then BA and AB are also matrices that are non-singular of the same order.

Theorem 3: This theorem says that the result of the product matrices is the same as the product of their individual determinants. For e.g. Take A and B as square matrices of the same order, then, |AB| = |A||B|.

Theorem 4: This theorem states that a square matrix is invertible only if it is a non-singular matrix.

**Elementary Row Transformation**

In this portion, you will learn about the elementary transformation process. In this process, the rows of the matrices are changed. There is no change in the columns. Make sure to refer to the rules related to elementary row transformation.

**Elementary Column Transformation**

In this portion, columns here are transformed leaving the rows constant. The same rules of the rows can be implemented into columns.

### Exercise-wise Discussion of RD Sharma Class 12 Maths Solutions Chapter 7- Adjoint and Inverse of a Matrix

- There are a total of two exercises in this chapter. The first exercise consists of 39 questions. The questions here are divided into sub-parts to ensure that you write all the steps.
- Exercise 7.2 has 16 questions that vary in difficulty. It tests your conceptual clarity. It is important to write every step to ensure that you attain the perfect score.
- The type of questions that you will be asked in the exercises includes- verify the statement from the given matrix, finding the adjoint of the matrix, etc.
- The exercises will give you an in-depth understanding of adjoint and inverse of a matrix. Make sure that you revise the formulas thoroughly before solving the exercises of the chapter.
- RD Sharma Class 12 Maths Solutions Chapter 7- Adjoint and Inverse of a Matrix will prove to be the most useful resource if you want to study the chapter in a comprehensive and thorough manner.

### Benefits of RD Sharma Class 12 Maths Solutions Chapter 7 by Instasolv

- Our subject matter experts have designed the RD Sharma Solutions for Class 12 Chapter 7 after a thorough research on the topics and past papers of CBSE.
- All the solutions adhere to the exam standards of CBSE and the current syllabus. These solutions will ensure that you are able to solve any question related to the topic matrices in your CBSE exams.
- This chapter is also important from the perspective of entrance exams like JEE and NEET so by referring to our solutions you are also preparing yourself for such exams.