Eigenvalues of Invertible Matrix

[sonic25]

Homework Statement

If A is an invertible nxn matrix, then A has n distinct eigenvalues. (TRUE/ FALSE)

Homework Equations

The Attempt at a Solution

True? We weren't really taught the concept of eigenvalues too well, but from what I can gather square matrices appear to have the same number of eigenvalues as their number of rows/columns. I'm not sure why though.

 

[AlephZero]

Is the unit nxn matrix invertible? What are its eigenvalues?

 

[HallsofIvy]

"number of eigenvalues" and "number of distinct eigenvalues" are two entirely different things. As far as being "invertible" is concerned the only thing you can say is that a matrix is invertible if and only if it does not have 0 as an eigenvalue.