9. How many of the following statements are true?
A prime multiplied by a prime is always a prime.
A square multiplied by a square is always a square.
An odd number multiplied by an odd number is always an odd number.
An even number multiplied by an even number is always an even number.
A 0
B 1
C 2
D 3
E 4
9. D The first statement is false. For example, 2 and 3 are primes, but their product is 6 which is not prime.
Two squares may be denoted by $m^{2}$ and $n^{2}$, where $m$ and $n$ are non-negative integers. Their product is $m^{2} n^{2}=(m n)^{2}$. So a square multiplied by a square is always a square. Two odd numbers may be denoted by $2 m+1$ and $2 n+1$, where $m$ and $n$ are integers. Their product is $(2 m+1)(2 n+1)=4 m n+2 m+2 n+1=2(2 m n+m+n)+1$, which is also odd. So an odd number multiplied by an odd number is always an odd number. Two even numbers may be denoted by $2 m$ and $2 n$, where $m$ and $n$ are integers. Their product is $4 m n=2(2 m n)$, which is also even.
So an even number multiplied by an even number is always an even number. Therefore three of the statements are true.