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On (\mathbb{Z}), (a*b=a+b-1). What is the inverse of (5)?(\mathbb{Z}) पर (a*b=a+b-1) है। (5) का प्रतिलोम क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-3)(-3)
Step 1: For identity (e), (a+e-1=a), so (e=1). Step 2: Put (5*b=1): (5+b-1=1), giving (b=-3). Step 3: While finding inverse, equate the result to the identity found, not automatically to zero.चरण 1: तत्समक अवयव (e) के लिए (a+e-1=a), इसलिए (e=1)। चरण 2: (5*b=1) रखें, (5+b-1=1) से (b=-3)। चरण 3: प्रतिलोम निकालते समय परिणाम को शून्य नहीं, बल्कि मिले हुए तत्समक अवयव के बराबर रखें।
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