does a rectangular matrix have an inverse?
I know all square matrices have easily to identify inverses, but does that continue on with rectangular matrices?
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$\begingroup$If $A$ is an $m\times n$ matrix with $m\neq n$, then $A$ cannot be both one-to-one and onto (by rank-nullity). So $A$ might have a left inverse or a right inverse, but it cannot have a two-sided inverse.
$\endgroup$ $\begingroup$Actually, not all square matrices have inverses. Only the invertible ones do. For example, $\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}$ does not have an inverse.
And no, non-square matrices do not have inverses in the traditional sense.
There is the concept of a generalized inverse. To very briefly summarize the link, an $n \times m$ matrix $A$ has an $m \times n$ generalized inverse, denoted $A^g$, if $A^g$ satisfies $A A^g A = A$.
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