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June 1, 202339 Insightful Publications

**NCERT Solutions for Class 12 Maths Chapter 3:** Mathematics is one of the subjects included in the Class 12 curriculum. Chapter 3 deals with matrices, types of matrices, and various operations that can be performed on them. The concept of matrices has a wide range of applications even in real life. Therefore, students should master it and solve the questions to have a deeper understanding.

The NCERT solutions for Class 12 Maths Chapter 3 that Embibe provides have all the solutions to every question asked. It also contains explanations and a step-wise approach to solving the problems for a better understanding. Embibe also allows students to learn, practice and test their knowledge through study materials like ebooks, 3D videos, questions, and mock tests. Scroll down to learn more about the NCERT solutions for Class 12 Maths Chapter 3.

Matrices is one of the most interesting chapters of all the topics provided in Class 12 Maths. Once the basics of the topic are understood, students will find problem-solving a fun-loving experience. Furthermore, practicing the solutions will become easy and smooth.

Embibe offers NCERT solutions to every question provided at the end of the textbooks designed considering the latest syllabus. Moreover, students can learn the concepts, practice more than 1500 questions, and take tests on Embibe for free to achieve higher marks in their exams.

Below, we have provided the list of topics included in this chapter:

Sl.No | Topics |
---|---|

1 | Basics of Matrices |

2 | Types of Matrices |

3 | Operation on Matrices |

4 | Symmetric and Skew-Symmetric Matrices |

5 | Elementary Operation (Transformation of a Matrix) |

6 | Inverse Matrix |

Every chapter has some important points and highlights that give a gist of the topics covered in it. Students can refer to them while revising their concepts. They can find the important points to remember for this chapter below.

- A set of numbers (real or imaginary) or symbols or expressions arranged in the form of a rectangular array of m rows and n columns is called m×n matrix.
- A square matrix A=[aij]n×n is called an identity or a unit matrix, if aij=0 for all i≠j and aij=1 for all i=j.
- Commutativity: If A and B are two matrices of the same order, then A+B=B+A.
- Associativity: If A,B,C are three matrices of the same order, then (A+B)+C=A+(B+C).
- Existence of Identity: The null matrix is the identity element for matrix addition i.e., A+O=A=O+A
- Existence of Inverse: For every matrix A=[aij]m×n, there exists a matrix −A=[−aij]m×n, such that A+(−A)=O=(−A)+A
- Cancellation Laws: If A,B,C are three matrices of the same order, then A+B=A+C⇒B=C and, B+A=C+A⇒B=C
- In order to find the inverse of a non-singular square matrix A by elementary operations, we write A=IA or A=AI
- We perform a sequence of elementary row operations successively on A on the LHS and the pre-factor I on RHS till we obtain. The matrix B, so obtained, is the desired inverse of matrix A.

The NCERT Class 12 solutions for all the chapters of Maths are provided below for students’ reference. By following the chapters along with the solutions, students can easily score good marks in the Class 12 Maths final exam.

- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Application of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability

After completing their learning of the chapter students may take the Class 12 Maths mock tests from Embibe. These mock tests will help students prepare for the exam in a better manner as they get to understand their level of preparation. Hence, students can continue practicing and score higher marks in the exam accordingly.

Here are some frequently asked questions about the NCERT solutions for Class 12 Maths Chapter 3:

**Ans**: Students can find NCERT solutions for Class 12 Maths Chapter 3 on Embibe.

**Ans:** The list of topics covered under NCERT solutions for Class 12 Maths Chapter 3 is mentioned on this page.

**Ans**: All the questions of the Matrices chapter of Class 12 Maths provided by Embibe come with detailed step-wise solutions. This helps them learn the process to solve problems systematically.

**Ans:** Students can take free mock tests for Class 12 Maths on Embibe.

**Ans:** The Chapter Matrices in Class 12 Maths is one of the easiest and most scoring chapters in Class 12 Maths.

*We hope you found this article useful. Stay tuned to Embibe for the latest updates and more such study resources.*