Compiler Design self Doubt

Question

"Every Regular Grammar has a Right linear grammar and this is LL(1)"

What is meaning of this statement exactly and does it hold always?

My Assumptions:

If a grammar is right linear grammar then it can be parser by LL(1)

 ->I am sure they are not left recursive.
-->There definitely exist one unambiguous grammar for that right linear grammar.
But this is not suffice to make grammar LL(1).

Correct if I assumed anything wrong with some intutive answer.

Comments

even though it is right linear, it may have ambiguity. This statement doesn't seem universally correct.

S -> A | B, A -> a, B-> a

Right linear regular grammar with ambiguity, thus not parsable by LL(1).

Answer 1

"Every Regular Grammar has a Right linear grammar and this is LL(1)"

Conditions for LL(1) :

1) unambiguous CFG .

2) left factored.

3) not left recursive.

If a grammar is Right linear then it is Not left recursive for sure.

But if the Right linear grammar is like this,

$S$ $→$ $aA$|$a$                                                                                                                                                               

$A$ $→$ $c$

Then this is not left factored grammar, hence Not LL(1), but there are some which can satisfy all the conditions and can be LL(1).