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On (\mathbb{R}), (a*b=a+b+ab). Which number does not have an inverse?समुच्चय (\mathbb{R}) पर (a*b=a+b+ab) है। किस संख्या का प्रतिलोम नहीं बनता?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-1)(-1)
Step 1: The identity is (0). Step 2: From (a*x=0), (a+x+ax=0), so (x=\frac{-a}{1+a}). Step 3: At (a=-1), the denominator is zero, so inverse does not exist.चरण 1: तत्समक (0) है। चरण 2: (a*x=0) से (a+x+ax=0), इसलिए (x=\frac{-a}{1+a})। चरण 3: (a=-1) पर हर शून्य हो जाता है, इसलिए प्रतिलोम नहीं है।
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