relation between matrix rref and inverse??

[cward22]

what is the relation between the rref and the inverse of a matrix?

i have that A matrix A of size (n,n) is invertible, if there is a matrix B such that AB=In=BA. In this case, B is called the inverse and is denoted A-1.

what does it mean when one matrix has an inverse and rref and the other does NOT have an inverse but has an rref??

also, how does the rref and the inverse relate to the det??

 

[pitoten]

I think any matrix can be converted into rref, but not every matrix has an inverse. If DET=0, there is no inverse, but there is still an rref.