# NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 Matrices in Hindi Medium as well as English Medium for UP Board (Intermediate students), CBSE & other Board based on latest CBSE Syllabus 2020-2021.

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Class: | 12 |

Subject: | Maths |

Chapter 3: | Exercise 3.1 |

### 12th Maths Exercise 3.1 Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 Matrices solutions in English & Hindi Medium are given below updated for new academic session 2020-21. You can download these solutions form the link given at the page. Get here all the exercises of Class 12 Mathematics Chapter 3 main page. Join the discussion forum to share your knowledge with the others in NIOS or CBSE Board concern.

### Exercise 3.1 Solutions in Hindi & English

#### Important Terms About Matrices

1. All main diagonal elements of a skew-symmetric matrix are zero.

2. Every square matrix can be uniquely expressed as the sum of a symmetric and a skew symmetric matrix.

3. All positive integral power of a symmetric are symmetric.

4. All odd positive integral power of a skew symmetric matrix are skew symmetric.

##### PROPERTIES OF MATRIX ADDITION

1. Commutativity: If A and B are two matrices of same order, then A + B = B + A.

2. Associativity: If A, B, C are three matrices of same order, then (A + B) + C = A + (B + C).

3. Existence of Identity: The null matrix is the identity element for matrix addition. A + O = O + A = A.

4. Existence of inverse: For every matrix A = [aij, there exists a matrix – A= [-aij] such that A + (-A) = O = (-A) + A.

5. Cancellation laws: If A, B, C are three matrices of the same order, then A + B = A + C implies that B = C and B + A = C + A implies that B = C.

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