Linear Algebra and Its Applications · Problem 2.4.16

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

(

A

paradox) Suppose

A

has a right-inverse

B

. Then

AB = I

leads to

A^T AB = A^T

B(A^T A)^{-1} A^T

. But that satisfies

BA = I

; it is a left-inverse. Which step is not justified?