Show that if A is invertible and AC =0 then C=0; similarly if C is invertible and AC=0 then A=0?

darn I meant A = [ 3 7] [ 0 0]

C = [ 0 1] [ 0 2 ]

C was originally that but I don't know if I am suppose to make it all zeroes

Are you asking in general, or in this specific case?

in this specific case?

but AC is not =0 here

Yes it is, it becomes a zero matrix. But they want me to show that C can also be a zero matrix and when multiplied with A will give a zero matrix as well.

if A is invertible I don't know how to show that

A is not invertible

C is not invertible

I realize that A is not invertible too

But okay for C though do you know what it means by C=0

Do they mean C is a 2 by 2 zero matrix?

you have C={0 1} {0 2}

Yeah but the question say show that if A is invertible and AC=0 then C=0

I can't show that A is invertible thats why I'm lost

but A isn't invertible AC={3 7} * {0 1} ={3*0+7*0 3*1+7*2}={0 17} {0 0} {0 2} {0*0+0*0 0*1+0*2} {0 0} im sorry but this case does not go with the above question? first of all it isn't invertible someting is wrong with your question it makes no sense second of all AC does not equal zero are these matrices the book or teacher gave you?

Its from a book

I guess thanks for your help anyways

so this wasn't some general thing you are suppose to prove right? the book actually gives you 2 matrices and tells you to do the above?

what is the name of the book?

Yes they gave me those two

Contemporary Linear Algebra

Here's the exact question

robert busby?

We showed in Ex. 3 that its possible to have nonzero matrices A and C for which AC=0. However show that if A is invertible and AC=0 then C=0; similarly if C is invertible and AC =0 then A=0

Yeah

and then they gave those two matrices in the example 3

what section

3.2 number 30

You have the book?

darn it sometimes you go through most of the book on amazon.com

well there's not much other information than what I've have provided

Yeah I can't get it to become invertible so I'll just leave it

Thanks for your help

im sorry ask your teach i like linear algebra but for that case the question made no sense

Yeah alright night!

night

I think theree's some confusion here. Ignore the specific matrices. The question is IN General, prove if A invertible and AC=0 then C=0: left multiply by A^-1 then AC = 0 becomes A^-1AC=0 which becomes C=0 Similarly for A if C invertible