The product of two numbers that are less than zero is also less than zero.

Is this a true and false question? if you have 2 numbers less then zero then you will be multiplying two negative numbers. and multiplying a negative by a negative gives a positive so that statement would be false. say for example you have - 2 x - 2 both numbers are less than 0 but - 2 x - 2 = 4 which is positive which is greater than zero.

No.

Their product is always greater than 0.