Answer sheets of meritorious students of class 12th’ 2012 M.P Board – All Subjects

February 14, 201339 Insightful Publications

**NCERT Solutions for Class 12 Maths Chapter 3:** Class 12 board exams are a turning point in a student’s life. Therefore, students must focus on practising NCERT Solutions for Class 12 Maths chapters. In this article, students can find the Class 12 NCERT Solutions Maths Chapter 3 Matrices. It is critical for students to go through Matrices chapter 3 solutions to answer all types of questions asked during board exams.

CBSE Class 12 Maths Chapter 3 talks about Types of Matrices, Equality of Matrices, Operations on Matrices, Addition and Multiplication of Matrices, Symmetric and Skew-Symmetric Matrices and Invertible Matrices. Also, Embibe offers a set of 375 practice questions for all the sub topics related to the Matrices chapter. To access free NCERT Solutions for Class 12 Chapter 3 Maths along with important topics, keep scrolling down!

Matrices is 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, practising 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 practice the questions at Embibe for free to acheive higher marks in their exams.

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

S.No | Topic Name |

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 |

Students 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 maximum marks in 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

**Q.1: Where can I find NCERT Solutions for Matrices topic of Class 12 Chapter 3 online? ****Ans**: Students can find Class 12 Maths Chapter 3 Matrices solutions for free on this page of Embibe. Following the solutions to all the in-text problems is the easiest way for the students to master the topics and score best marks.

**Q.2: Are all the NCERT solutions for Class 12 Maths chapters provided by Embibe for free?****Ans**: Yes, the NCERT solutions for all the chapters of Class 12 Maths provided by Embibe are for free. Also, students can find informative videos to learn Matrices concepts from Embibe.

**Q.3: What are the benefits of solving NCERT solutions for Class 12 Maths chapter 3 from Embibe?****Ans**: Firstly, all the questions of the Matrices chapter of Class 12 Maths provided by Embibe come with detailed step-wise solutions. Secondly, students can decode the solutions easily and they will become confident in answering any type of questions asked in the exam.

**Q.4: Are Matrices of Class 12 Maths Chapter 3 the easiest topic?****Ans**: Yes, Chapter 3 is one of the easiest chapters of the Maths syllabus, However, students must focus on practising all the NCERT solutions to master the topic of Matrices.

**Q.5: What are the Matrices topics in Class 12 Maths Chapter 3? ****Ans**: Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation on matrix, and invertible matrices.