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If (a*b=a+b+kab) and (k\neq0), which element will not have an inverse?यदि (a*b=a+b+kab) और (k\neq0), तो किस अवयव का प्रतिलोम नहीं होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-\frac{1}{k})(-\frac{1}{k})
Step 1: The identity of this operation is (0). Step 2: For inverse (b), (a+b+kab=0), hence (b(1+ka)=-a). Step 3: When (a=-\frac{1}{k}), (1+ka=0), so no inverse exists.चरण 1: इस संक्रिया का तत्समक अवयव (0) है। चरण 2: प्रतिलोम (b) के लिए (a+b+kab=0), इसलिए (b(1+ka)=-a)। चरण 3: जब (a=-\frac{1}{k}), तब (1+ka=0) हो जाता है और प्रतिलोम नहीं मिलता।
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