これいいね
Matrix Right inverse implies left inverse and vice versa Garth Isaak
右逆から左を出す
どうやるのか、調べていたら、これがあった

https://www.lehigh.edu/~gi02/m242/08m242lrinv.pdf
Right inverse implies left inverse and vice versa Garth Isaak
Notes for Math 242, Linear Algebra, Lehigh University fall 2008

These notes review results related to showing that if a square matrix A has a right inverse
then it has a left inverse and vice versa. We begin by reviewing the result from the text
that for square matrices A we have that A is nonsingular if and only if Ax = b has a unique
solution for all b.

Nonsingular if and only if unique solutions

Left inverse if and only if right inverse

(参考)
https://www.lehigh.edu/~gi02/f08m242.html
Fall 2008 Math 242 at Lehigh University Garth Isaak

https://www.lehigh.edu/~gi02/m242/08m242syl.pdf
Course Syllabus Garth Isaak

https://www.researchgate.net/profile/Garth-Isaak/2
ResearchGate
Garth Isaak
Lehigh University ・ Department of Mathematics
Ph.D.