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On (\mathbb{R}), (a*b=a+b-2ab). Which element will not have an inverse?(\mathbb{R}) पर (a*b=a+b-2ab) है। किस अवयव का प्रतिलोम नहीं होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{2})(\frac{1}{2})
Step 1: The identity is (0). Step 2: For inverse (b), (a+b-2ab=0), so (b(1-2a)=-a). Step 3: If (a=\frac{1}{2}), then (1-2a=0), so the inverse equation cannot be solved.चरण 1: तत्समक अवयव (0) है। चरण 2: प्रतिलोम (b) के लिए (a+b-2ab=0), जिससे (b(1-2a)=-a)। चरण 3: यदि (a=\frac{1}{2}), तो (1-2a=0) हो जाता है और समीकरण हल नहीं होता।
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