Data Sufficiency

Hi everyone,

I'm a little confused regarding the correct answer for the below mentioned question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer.
(2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder?
When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks.
Kash.