If $a < b$, which of the following are always correct?
1) $a^3< a^2b$
The answer to this question would be true because there is theorem that "If $a < b$ and we add the same positive number to both sides of the inequalitie, this would not effect the inequality."
Now the second problem is interesting:
2) $a^2 < ab$
Now there is also another theorem that says "If $a < b$ and we multiply the same positive number on both sides this would not effect the inequality."
Now, as it is specified on the top of the question:$a < b$. now in this question we are multiplying a on both sides which makes it $a^2 < ab$ so this should be correct. But, in the answers at the end of the book, the question number of this question is not given. Please help.