- #1

- 162

- 0

a. Show that if A is invertible and AB = 0, then

B = 0.

If A is invertible, it can be reduced to the I matrix.

Thus IB=0 (this is the part where I'm hesitant, can I say that IB=0?)

Thus B=0 since I≠0

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- Thread starter charlies1902
- Start date

- #1

- 162

- 0

a. Show that if A is invertible and AB = 0, then

B = 0.

If A is invertible, it can be reduced to the I matrix.

Thus IB=0 (this is the part where I'm hesitant, can I say that IB=0?)

Thus B=0 since I≠0

- #2

- 3,472

- 251

a. Show that if A is invertible and AB = 0, then

B = 0.

If A is invertible, it can be reduced to the I matrix.

Thus IB=0 (this is the part where I'm hesitant, can I say that IB=0?)

Thus B=0 since I≠0

How did you reduce A to the I matrix? What operation(s) did you perform?

- #3

- 162

- 0

How did you reduce A to the I matrix? What operation(s) did you perform?

Multiplying A^-1 to both sides. Is this necessary to state in the proof?

When I got the BI=0, I think I got it for the wrong reasons. I'm not very good at proofs. It took me awhile to think of multiplying A^-1 to both sides that that's how it justified BI=0. Typically when you go about doing proofs, how do you think in the "right" direction? Proofs seem to be so open ended compared to computation problems, that if you're not thinking in the "right" direction, it might take you a very long time to get it. Do you have any tips?

- #4

HallsofIvy

Science Advisor

Homework Helper

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Yes, it is necessary! That is, in fact, exactly what you are doing.Multiplying A^-1 to both sides. Is this necessary to state in the proof?

No, you do NOT get "BI= 0". You had AB= 0 and you multiply each side by AWhen I got the BI=0, I think I got it for the wrong reasons. I'm not very good at proofs. It took me awhile to think of multiplying A^-1 to both sides that that's how it justified BI=0.

Yes, proofs requireTypically when you go about doing proofs, how do you think in the "right" direction? Proofs seem to be so open ended compared to computation problems, that if you're not thinking in the "right" direction, it might take you a very long time to get it. Do you have any tips?

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