Inverse Element

If, for an operation, one element is the inverse element to the other, we get the identity element if we put both of them into the operation.

(+2) + (-2) = 0

  • 0 is the identity element for addition
  • The additive inverse element for +2 is -2.
  • The additive inverse element for -2 is +2.

2 * \dfrac {1}{2} = 1

  • 1 is the identity element for multiplication
  • The multiplicative inverse element for 2 is 1/2.
  • The multiplicative inverse element for 1/2 is 2.

Appendix

The exercise below contains an idea that appears in dimensional analysis, that’s where you multiply by 2.54 to go from inches to centimeters.

We intentionally make it more complicated–our motivation is to show you something simple and sensible here, and years from now when we show you something in tensors, we will say “hey guys, this is just like what you saw back there!”

10 * 1 unit

(1)10 * 1 unit

(\dfrac{2.54}{1} \dfrac{1}{2.54})10 * 1 unit

(\dfrac{2.54}{1} 10 \dfrac{1}* {2.54} 1 unit