Show that if m×n=1 then m=n=1 or m=n=-1

Given that m \times n = 1, we want to show that m = n = 1 or m = n = -1.

Let's assume that m and n are integers.

If m = 1 and n = 1, then m \times n = 1 \times 1 = 1, which satisfies the given condition.

If m = -1 and n = -1, then (-1) \times (-1) = 1, which also satisfies the given condition.

Let's consider the case where m and n are not both equal to 1 or both equal to -1.

Assume without loss of generality that m = 1 and n = -1. Then we have m \times n = 1 \times (-1) = -1 \neq 1.

Therefore, the only solutions for m \times n = 1 are m = n = 1 or m = n = -1.

\textbf{Answer:} m = n = 1 or m = n = -1