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On (A={0,1}), the operation (a*b) is ordinary multiplication. Which element has no inverse?समुच्चय (A={0,1}) पर क्रिया (a*b) को साधारण गुणन माना गया है। कौन-सा अवयव प्रतिलोम नहीं रखता?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (0)(0)
Step 1: Under ordinary multiplication, the identity is (1). Step 2: The inverse of (1) is (1) because (1\cdot 1=1). Step 3: (0\cdot x) can never become (1), so (0) has no inverse.चरण 1: साधारण गुणन में तत्समक (1) है। चरण 2: (1) का प्रतिलोम (1) है क्योंकि (1\cdot 1=1)। चरण 3: (0\cdot x) कभी (1) नहीं बन सकता, इसलिए (0) का प्रतिलोम नहीं है।
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