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Chapter 1: Problem 22

What is the identity element for multiplication?

Short Answer

Expert verified
The identity element for multiplication is \(1\), as any number multiplied by one equals the same number (\(x \times 1 = x\)).

Step by step solution

01

Understand the identity element

An identity element, in mathematical operations, is a value which, when combined with any other value in a specific operation, doesn't change the original value.
02

Determine the identity element for multiplication

In the context of multiplication, the identity element must satisfy this condition: for any number \(x\), when multiplied by the identity element, the result is still \(x\). Mathematically, the equation should be \(x \times \text{identity} = x\).
03

Identify the identity element

Since we know that any number multiplied by one equals the same number (\(x \times 1 = x\)), the identity element for multiplication is \(1\).

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