Cross product of dfa in toc

Question

if a automata in dfa contains N states and further automatic contains  M states then in the final DFA obtained from cross product method will contain N*M States.

First ,is the above statement always true and if it is then will there be a need to minimize it after cross product to get minimal dfa in questions which asks for more than one condition to exist in dfa.

Comments

from where you read this statement ?

Answer 1

The statement is incorrect.

After performing cross product between two DFA’s we need to check for minimization.

But most of the time we get minimized DFA only.