1
Question
If 𝐴+𝐵=𝐴𝐵 then 𝐴𝐵=𝐵𝐴
If 𝐴+𝐵=𝐴𝐵 then 𝐴𝐵=𝐵𝐴
Open in App
Solution
Consider the expression(𝐴−1)(𝐵−1)=𝐴𝐵−𝐴−𝐵+1=1Thus (𝐴−1) and (𝐵−1) are inverse to each other, whence1=(𝐵−1)(𝐴−1)=𝐵𝐴−𝐴−𝐵+1It follows that𝐵𝐴=𝐴+𝐵=𝐴𝐵
Consider the expression
(𝐴−1)(𝐵−1)=𝐴𝐵−𝐴−𝐵+1=1
Thus (𝐴−1) and (𝐵−1) are inverse to each other, whence
1=(𝐵−1)(𝐴−1)=𝐵𝐴−𝐴−𝐵+1
It follows that
𝐵𝐴=𝐴+𝐵=𝐴𝐵
Suggest Corrections
1
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
