Question

Let \(A\) be a \(2 \times 2\) matrix. For every two-dimensional vector \(v\), there exists a two-dimensional vector \(w\) such that
\(Aw=v\)
Show that \(A\) is invertible.

Thank you!

Answer 1

As long as determinate of A is not zero, then A has an inverse

Answer 2

@dumbcow How do I show that, though?

Answer 3

@zmudz It's something that has been proven.