# Why are invertible matrices "one-to-one"?

##### 1 Answer

Dec 20, 2015

#### Answer:

See explanation...

#### Explanation:

I think the question is referring to the natural use of a matrix to map points to points by multiplication.

Suppose

Suppose further that

Then multiplying both sides by

#p_1 = I p_1 = M^(-1)M p_1 = M^(-1)M p_2 = I p_2 = p_2#

So:

#Mp_1 = Mp_2 => p_1 = p_2#

That is: multiplication by