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# NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 Determinants cover the important concept of inverse and adjoint of a matrix. The adjoint of a square matrix is defined as the transpose of its cofactor matrix. The adjoint of matrix A is denoted by adj A. There are a total of four theorems explained in these solutions based on the adjoint of a matrix. The first theorem states that when A is any given square matrix of order n, then A(adj A)=(adj A)A= AI. Theorem two states that when A and B are non-singular matrices of the same order, then AB and BA both are also non-singular matrices of the same order. The third theorem states that the determinant of the product of matrices is equal to the product of their respective determinants, that is, AB= |A| |B|, where A and B are Square Matrices of the same order. The fourth and the last theorem included in this exercise states that A square matrix A is invertible if and only if A is a non-singular matrix. Notes provided in Class 12 NCERT Solutions Maths Chapter 3 will help students to clearly apply these theorems to find the inverse of a matrix.

There are a total of 18 questions provided in this exercise related to finding the inverse of a matrix by using the adjoint. Solving the questions incorporated in NCERT Solutions for Class 12 Maths Chapter 4 is adequate to attain an in-depth knowledge of methods as well as theorems required to find adjoint and inverse of determinants. They are also an efficient resource to promote the error-free learning of complex concepts. Students can download and practice these NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 that is available in a scrollable PDF format given below.

**☛** Download NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5

**Exercise 4.5 Class 12 Chapter 4 **

### More Exercises in Class 12 Maths Chapter 4

- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.1
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.2
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.3
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.4
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.6
- NCERT Solutions Class 12 Maths Chapter 4 Miscellaneous Exercise

## NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 Tips

NCERT solutions Class 12 Maths Chapter 4 Exercise 4.5 are framed in a simple and easy-to-understand pattern to help students score higher in exams. These resources are an excellent way to achieve great results. Students must attempt all the questions provided in these solutions to understand concepts thoroughly. It will also enable them to get an idea of the type of problems that can be framed in an examination.

By solving the sums provided in the Class 12 NCERT Solutions Maths Chapter 4, kids will know how much time they need to prepare each topic. They can always use these step-wise solutions to clear their doubts wherever needed. The interactive format of the NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 is highly prominent in enhancing the speed and accuracy of performing calculations. It is advisable to implement the practice of complex topics for attaining deep knowledge.

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