Which of the following statement are true? (i) The product of a positive and negative integer is negative. (ii) The product of three negative integers is a negative integer. (iii) Of the two integers, if one is negative, then their product must be positive. (iv) For all non-zero integers $a\text{and}b,a\times b$ is always greater than either $a\text{or}b.$ (v) The product of a negative and a positive integer may be zero. (vi) There does not exist an integer $b$ such that for $a>1,a\times b=b\times a=b.$

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