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You can multiply each side of the multiplicative inverse equation by the other inverse to show that any two multiplicative inverses are equal. Here it is more formally.
Theorem: For all x in R, there exists y in R s.t. x * y = 1. If there is a y' in R such that x * y' = 1, then y = y'.
Proof:
- Start with x * y = 1.
- y * x = 1 (commutative)
- (y * x) * y' = 1 * y' = y'
- y * (x * y') = y' (associative)
- y * 1 = y' (because x*y' = 1)
- y = y'
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What is the multiplicative of -1?
Assuming the question is about the multiplicative inverse, the answer is, -1. It is its own multiplicative inverse.
How do you prove the multiplicative inverse of a real number is unique?
To prove the uniqueness of the multiplicative inverse of a real number, let's assume that there are two different multiplicative inverses, say a and b, for a given real number x. This means that a * x = b * x = 1. By multiplying both sides of the equations by the common factor x, we get a = b = 1/x, which proves that the multiplicative inverse is indeed unique.
What is the multiplicative inverse of 4 i?
The multiplicative inverse of 4i is -(1/4)*i.
What is the multiplicative inverse of −100?
the multiplicative inverse of -100 is 1/-100
What is an multiplicative inverse of -.50?
The multiplicative inverse is 1/(-0.50) = -2
Name the additive inverse and the multiplicative inverse for the number 2.5?
Additive inverse: -2.5 Multiplicative inverse: 0.4
What is zero product property?
Multiplicative Inverse of a NumberReciprocal The reciprocal of x is . In other words, a reciprocal is a fraction flipped upside down. Multiplicative inverse means the same thing as reciprocal. For example, the multiplicative inverse (reciprocal) of 12 is and the multiplicative inverse (reciprocal) of is . Note: The product of a number and its multiplicative inverse is 1. Observe that ·= 1. Multiplicative Inverse of a NumberReciprocal The reciprocal of x is . In other words, a reciprocal is a fraction flipped upside down. Multiplicative inverse means the same thing as reciprocal. For example, the multiplicative inverse (reciprocal) of 12 is and the multiplicative inverse (reciprocal) of is . Note: The product of a number and its multiplicative inverse is 1. Observe that ·= 1.
What is the multiplcative inverse of negative 3?
The reciprocal (multiplicative inverse) of -3 is -1/3.The reciprocal (multiplicative inverse) of -3 is -1/3.The reciprocal (multiplicative inverse) of -3 is -1/3.The reciprocal (multiplicative inverse) of -3 is -1/3.
Multiplicative inverse of a negative number?
The multiplicative inverse is the negative of the reciprocal of the positive value. Thus the multiplicative inverse of -7 is -1/7.
What is the multiplicative inverse of 625?
The multiplicative inverse of 625 is 1/625 or 0.0016
What is the multiplicative inverse of negative 9?
-9; the multiplicative inverse: -1/9
What is an example of multiplicative inverse?
A multiplicative inverse is the same as a reciprocal. The multiplicative inverse of x is 1/x. So, the multiplicative inverse of 4 is 1/4; or 7 is 1/7 and of 0.2 is 1/0.2 = 5.
