**RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3: **The identity elements for binary operations are explained in the third exercise in Chapter 3. The **RD Sharma Solutions for Class 12 Chapter 3** Exercise 3.3 are provided in easy-to-understand language, which increases students’ grasping ability. Students can refer to **RD Sharma Solutions Class 12 Maths** Chapter 3 Binary Operations Exercise 3.3 PDF, which is available here, for more understanding on the concepts covered in this exercise.

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## Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 PDF

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3

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### Access RD Sharma Solutions For Class 12 Maths Chapter 3 – Binary Operations Exercise 3.3 Questions With Solution

**1. Find the identity element in the set I ^{+} of all positive integers defined by a * b = a + b for all a, b ∈ I^{+}.**

**Solution:**

Let e be the identity element in I^{+} with respect to * such that

a * e = a = e * a, ∀ a ∈ I^{+}

a * e = a and e * a = a, ∀ a ∈ I^{+}

a + e = a and e + a = a, ∀ a ∈ I^{+}

e = 0, ∀ a ∈ I^{+}

Thus, 0 is the identity element in I^{+} with respect to *.

**2. Find the identity element in the set of all rational numbers except – 1 with respect to * defined by a * b = a + b + ab**

**Solution:**

Let e be the identity element in I^{+} with respect to * such that

a * e = a = e * a, ∀ a ∈ Q – {-1}

a * e = a and e * a = a, ∀ a ∈ Q – {-1}

a + e + ae = a and e + a + ea = a, ∀ a ∈ Q – {-1}

e + ae = 0 and e + ea = 0, ∀ a ∈ Q – {-1}

e (1 + a) = 0 and e (1 + a) = 0, ∀ a ∈ Q – {-1}

e = 0, ∀ a ∈ Q – {-1} [because a not equal to -1]

Thus, 0 is the identity element in Q – {-1} with respect to *.

**Binary Operations Ex 3.3 Q3****Binary Operations Ex 3.3 Q4**

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There are a total of 4 questions in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3.

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