Looking for NCERT Solutions for Class 12 Maths Exercise 3.3? If yes then you are in the right place. Here we have provided you with the Question and Answers of Exercise 3.3. These solutions are written by expert teachers and are so accurate to rely on.

Chapter | 3. Matrics |

Exercise | 3.3 |

Class | Twelve |

Subject | Maths |

Category | NCERT Solutions for Class 12 |

NCERT Solutions for Class 12 Maths are available online for students to use and refer to while studying for their exams. The solutions provide step-by-step explanations for each problem in the textbook, making it easy for students to understand the concepts. With Class 12 Maths NCERT Solutions, students can be sure that they are getting the most accurate and up-to-date information available. The solutions are regularly updated by experts in the field, so students can be confident that they are using the most current information.

## NCERT Solutions for Class 12 Maths Exercise 3.3

### Matrics Solutions

**Q 1) Find the transpose of each of the following matrices:**

**Answer)**

**Q 2) If** **then verify that:**

**(i) (A + B)’ = A’ + B’****(ii) (A – B)’ = A’ – B’**

**Answer)**

**Q 3) If** **then verify that:**

**(i) (A + B)’ = A’ + B’****(ii) (A – B)’ = A’ – B’**

**Answer)**

**Q 4) If** ** then find (A + 2B)’.**

**Answer)**

**Q 5) For the matrices A and B, verify that (AB)’ = B’A’, where:**

**Answer)**

**Q 6) (i) If A =** **then verify that A’A = I.**

**(ii) If A =** **then verify that A’A = I.**

**Answer)**

**Q 7) (i) Show that the matrix A =** **is a symmetric matrix.**

**(ii) Show that the matrix A =** **is a skew symmetric matrix.**

**Answer)**

**Q 8) For a matrix A =** **verify that:**

**(i) (A + A’) is a symmetric matrix.****(ii) (A – A’) is a skew symmetric matrix.**

**Answer)**

**Q 9) Find 1/2 (A + A’) and 1/2(A – A’) when A =**

**Answer)**

**Q 10) Express the following matrices as the sum of a symmetric and skew symmetric matrix:**

Answer)

**Q 11) If A and B are symmetric matrices of same order, AB – BA is a:**

**(A) Skew-symmetric matrix****(B) Symmetric matrix****(C) Zero matrix****(D) Identity matrix**

**Answer)**

Given: A and B are symmetric matrices ∴ A = A’ and B = B’

Now, (AB – BA)’ = (AB)’ – (BA)’ ∴ (AB – BA)’ = B’A’ – A’B’ [Reversal law]

∴ (AB – BA)’ = BA – AB [From eq. (i)] ∴ (AB – BA)’ = – (AB – BA)

∴ (AB – BA) is a skew matrix.

Therefore, option (A) is correct.

**Q 12) If A =** **, then A + A’ = I, if the value of α is:**

**(A) π/6****(B) π/3****(C) π****(D) 3π/2**

**Answer)**

Therefore, option (B) is correct.

That’s it. These were the solutions of NCERT Class 12 Maths Exercise 3.3. Our team hopes that you have found these solutions helpful for you. If you have any doubt related to this chapter then feel free to comment your doubts below. Our team will try their best to help you with your doubts.