Hello Students! In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 3.3**.

You can download the **PDF of NCERT Books Maths Chapter 3** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 3.3**.

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If you want to recall **All Maths Formulas for Class 12**, you can find it by clicking this link.

If you want to recall **All** **Maths Formulas for Class 11**, you can find it by clicking this link.

**NCERT Solutions for Maths Class 12 Exercise 3.1**

**NCERT Solutions for Maths Class 12 Exercise 3.2**

**NCERT Solutions for Maths Class 12 Exercise 3.4**

**NCERT Solutions for Maths Class 12 Exercise 3.3**

**Maths Class 12 Ex
3.3 Question 1.**

**Find the transpose of each of the following matrices:**

**Solution:**

**Maths Class 12 Ex
3.3 Question 2.**

**If**

**then verify that:**

**(i) (A + B)’ = A’ + B’**

**(ii) (A – B)’ = A’ – B’**

**Solution:**

We have,

**Maths
Class 12 Ex 3.3 Question 3.**

**If**

**then verify that:**

**(i) (A + B)’ = A’ + B’**

**(ii) (A – B)’ = A’ – B’**

**Solution:**

**Maths
Class 12 Ex 3.3 Question 5.**

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

**Solution:**

**Maths Class 12 Ex
3.3 Question 6.**

**(i) If**

**, then verify that A’A = I**

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

**Solution:**

**(i)**We have,

**Maths Class 12 Ex
3.3 Question 7.**

**(i) Show that the matrix**

**is a symmetric matrix.**

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

**Solution:**

**(i) **For a symmetric matrix a_{ij} =
a_{ji}

Now,

Here, a_{12}
= –1 = a_{21}, a_{13} = 5 = a_{31}, a_{23} = 1
= a_{32}

Again,
a_{11}, a_{22}, a_{33} are 1, 2, 3, respectively.

Hence, a_{ij}
= a_{ji}

**Maths Class 12 Ex
3.3 Question 8.**

**For the matrix,**

**, verify that**

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

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

**Solution:**

**Maths Class 12 Ex
3.3 Question 9.**

**Solution:**We have,

**Maths Class 12 Ex
3.3 Question 10.**

**Express the following matrices as the sum of a symmetric and a skew-symmetric matrix.**

**Solution:**

**Choose the
correct answer in the following questions:**

**Maths Class 12 Ex
3.3 Question 11.**

**If A, B are symmetric matrices of same order, then AB – BA is a**

**(A) Skew symmetric matrix**

**(B) Symmetric matrix**

**(C) Zero matrix**

**(D) Identity matrix**

**Solution:**

Since A and B are symmetric matrices, A’ = A and B’ = B.

Then, (AB – BA)’ = (AB)’ – (BA)’

= B’A’ – A’B’

= BA – AB

= –(AB – BA)

Therefore, AB – BA is a skew-symmetric matrix.

Hence, option (A)
is correct.

**Maths Class 12 Ex
3.3 Question 12.**

**If**

**, then A + A’ = I, if the value of Î± is**

**(A) Ï€/6 (B) Ï€/3 (C) Ï€ (D) 3Ï€/2**

**Solution:**

We have,

**Related Links:**

**NCERT Solutions for Maths Class 12 Exercise 3.1**

**NCERT Solutions for Maths Class 12 Exercise 3.2**

**NCERT Solutions for Maths Class 12 Exercise 3.4**