Question

Prove that a square matrix is invertible if and only if it has a full rank.

Answer 1

Let we have invertible n byn matrix A, then det A is nonzero. So, there is minor of size n, hence A has
full rank.
Conversely, if A has full rank then there is minor of size n, hence A has
nonzero det A, and we can explicitely compute A^-1, so A is invertible.