Question
is there an integer that is its own inverse?
Answers
GPT-4o mini
Yes, an integer can be its own inverse in the context of certain operations. For example, with respect to the operation of addition, an integer \( x \) is its own inverse if:
\[
x + x = 0
\]
This means \( x \) must equal 0, since \( 0 + 0 = 0 \).
In the context of multiplication, an integer \( x \) is its own inverse if:
\[
x \times x = 1
\]
In this case, the only integers that satisfy this equation are 1 and -1, since:
\[
1 \times 1 = 1 \quad \text{and} \quad (-1) \times (-1) = 1
\]
So, the integers that are their own inverses are 0 with respect to addition, and 1 and -1 with respect to multiplication.
\[
x + x = 0
\]
This means \( x \) must equal 0, since \( 0 + 0 = 0 \).
In the context of multiplication, an integer \( x \) is its own inverse if:
\[
x \times x = 1
\]
In this case, the only integers that satisfy this equation are 1 and -1, since:
\[
1 \times 1 = 1 \quad \text{and} \quad (-1) \times (-1) = 1
\]
So, the integers that are their own inverses are 0 with respect to addition, and 1 and -1 with respect to multiplication.