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Q: Is it true that for any two nonzero integers the product and quotient have the same sign and why?

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That is because that is how the product and quotient are defined.

True.

Yes, it is.

yes

Those are the rules of multiplication (and division).

It follows from the definitions of the two operations.

-- Their sum and difference both have the same sign that the two integers have. -- Their product and quotient are both positive.

The product or quotient of two numbers that have the same sign is positive. The product or quotient of two numbers with different signs is negative.

-- If the two integers have the same sign, their quotient is positive. -- If the two integers have different signs, their quotient is negative.

To find the Quotient and Product of two integers this is how it works if the two numbers are the same sign then it would be a postivite answer but if the two number has different signs the answer would be negative but that is only with muilty and divison

The quotient has a positive sing in that case.

Their quotient is positive if the integers have the same sign;negative if the integers have different signs;zero if the dividend is zero (and the divisor is not).

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