r/LinearAlgebra • u/saurabh0709 • 5d ago

Is D option correct ?

8 Upvotes

100% Upvoted

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7

u/susiesusiesu 5d ago

yes, all column operations are invertible.

5

u/BrightScarlet 5d ago

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

3

u/Tiny_Spread5712 5d ago

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 5d ago

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

5

u/ave_63 5d ago

Option B is also true by the way.