I am studying conversion from left recursive grammar to right recursive grammar. The given grammar is
$$E \to E + T \mid T $$
It's equivalent right recursive grammar will be $$\begin{align}E &\to TA\\ A &\to +TA \mid \epsilon\\ \end{align}$$
I understood this, that it is derived from changing the grammar $A \to Aa \mid b$ to its equivalent right recursive grammar and then comparing it accordingly. But why the right recursive grammar for this grammar is not
$$E \to T + E \mid E$$
As it also generates the same language and when there is only addition in an equation then associativity doesn't matter. Why can't this grammar be the equivalent right recursive grammar?