Identify an example where A B = C B while A C .

Step-by-step solution

Checking the given options for the condition A B = C B and A C . For the first option: A B = ( i + j ) i = 1 C B = ( i - j ) i = 1 Here, A B = C B = 1 . Also, i + j i - j , so A C . For the second option: A B = (2 i + j ) i = 2 C B = ( i - j ) i = 1 Here, A B C B . For the third option: A = i + j and C = i + j Here, A = C , which violates the given condition. For the fourth option: A B = i i = 1 C B = k i = 0 Here, A B C B . The first option satisfies all the given conditions.