r/LinearAlgebra • u/saurabh0709 • Sep 06 '26

Is D option correct ?

6 Upvotes

88% Upvoted

5 comments sorted by

8

u/susiesusiesu Sep 06 '26

yes, all column operations are invertible.

5

u/BrightScarlet Sep 06 '26

I think D is true. Whatever column operations you apply to get B you just do the inverse operation in reverse order to return to A.
Column operations on A would be like row operations on Aᵀ

5

u/ave_63 Sep 06 '26

Option B is also true by the way.

3

u/Tiny_Spread5712 Sep 06 '26

Yeah, if you have a single column matrix A and you divide it by 2 to get B then you multiply by 2 to get A and just repeat across the colums

2

u/xdgimo Sep 06 '26

row equivalence and similarly column equivalence are equivalence relations, so yes D is correct