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For (a*b=a+b-ab) on real numbers, which element does not have an inverse?वास्तविक संख्याओं पर (a*b=a+b-ab) में कौन सा अवयव प्रतिलोम नहीं रखता?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: The identity element is (0). Step 2: From (a*x=0), (a+x-ax=0), so (x=-\frac{a}{1-a}). Step 3: When (a=1), the denominator becomes (0), so the inverse does not exist.चरण 1: तत्समक अवयव (0) है। चरण 2: (a*x=0) से (a+x-ax=0) और (x=-\frac{a}{1-a}) मिलता है। चरण 3: (a=1) पर हर (0) हो जाता है इसलिए प्रतिलोम नहीं मिलता।
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