Exercise 3.5.23

As in Problem 22: Row space basis $(3,0,3),(1,1,2)$; column space basis $(1,4,2)$, $(2,5,7)$; the rank of ( 3 by 2 ) times ( 2 by 3 ) cannot be larger than the rank of either factor, so rank $\le 2$ and the 3 by 3 product is not invertible.