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

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Answer to a math question Show that if m×n=1 then m=n=1 or m=n=-1

$Expert avatar$

Hermann

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126 Answers

Given that

m \times n = 1

, we want to show that

m = n = 1

m = n = -1

.

Let's assume that

and

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

and

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

m = n = -1

.

\textbf{Answer:}

m = n = 1

m = n = -1

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

Answer to a math question Show that if m×n=1 then m=n=1 or m=n=-1

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