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On (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)) is defined. Which element is the inverse of (6), if the identity is (1)?समुच्चय (A={1,2,3,6}) पर (a*b=\operatorname{lcm}(a,b)) परिभाषित है। कौन सा अवयव (6) का प्रतिलोम है, यदि तत्समक (1) है?
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Correct answer:सही उत्तर: Noneकोई नहीं
Step 1: For inverse (x), (\operatorname{lcm}(6,x)=1) is required. Step 2: The least common multiple with (6) can never be (1). Step 3: Having an identity does not mean every element has an inverse.चरण 1: प्रतिलोम (x) के लिए (\operatorname{lcm}(6,x)=1) चाहिए। चरण 2: (6) के साथ लघुत्तम समापवर्त्य कभी (1) नहीं हो सकता। चरण 3: हर तत्समक वाली क्रिया में हर अवयव का प्रतिलोम होना जरूरी नहीं है।
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