How come only square matrices have inverses?

Question

How come only square matrices have inverses?

Answer 1

My mattress is rectangular and has 2 sides. One topside and an underbelly.

Answer 2

Cause it'd be uneven if you tried it with non-square ones.... like for 2x2 there's the 1/(ad-bc) thing, and there's a formula for 3x3.... but there's nothing for 2x1 or 2x3. Don't know what the reasont for that is actually... sorry haha.  

Answer 3

an n-by-n (square) matrix A is called invertible or non-singular if there exists an n-by-n matrix B such that A*B = B*A = I  (A is the regular matrix B is the inverse and I is the Identity matrix)

Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse.  in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA=I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB=I.