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Matrix algebra help

Quick question on multiplication. in fp1 4G question 4 (page 98) the question says

"given that ABC = I, prove that B^-1 = CA."

This is a misprint right? B^-1 = AC is correct, right?
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TeeEm
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Original post by jpepsred
Quick question on multiplication. in fp1 4G question 4 (page 98) the question says

"given that ABC = I, prove that B^-1 = CA."

This is a misprint right? B^-1 = AC is correct, right?


C23.jpg
Reply 2
Avatar for Zacken
Zacken
22
Original post by jpepsred
Quick question on multiplication. in fp1 4G question 4 (page 98) the question says

"given that ABC = I, prove that B^-1 = CA."

This is a misprint right? B^-1 = AC is correct, right?


Nopes. Not a misprint. B=A−1IC−1=A−1C−1B = A^{-1} I C^{-1} = A^{-1}C^{-1}, so... what's B−1B^{-1}?
Original post by jpepsred
Quick question on multiplication. in fp1 4G question 4 (page 98) the question says

"given that ABC = I, prove that B^-1 = CA."

This is a misprint right? B^-1 = AC is correct, right?


No misprint, I'm afraid. ABC=1ABC = 1 gives you BC=A−1BC = A^{-1} and then C=B−1A−1C = B^{-1}A^{-1}, whence CA=B−1CA = B^{-1}.
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jpepsred
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Original post by TeeEm
C23.jpg


??
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TeeEm
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Original post by jpepsred
??


what book?
Do you think we all the same books ?
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jpepsred
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I think I know where I've gone wrong. I did this:
ABC = I
A B^-1 B C = B^-1 I
A C = B^-1

Of course you can't do that. It has to be written like this:

(AB)C = I or A(CB) = I

Either way, you can't "divide" by B in the first step. Amirite?
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jpepsred
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Original post by TeeEm
what book?
Do you think we all the same books ?


Ah, an OCR ******.
Reply 8
Avatar for Zacken
Zacken
22
Original post by jpepsred
I think I know where I've gone wrong. I did this:
ABC = I
A B^-1 B C = B^-1 I
A C = B^-1

Of course you can't do that. It has to be written like this:

(AB)C = I or A(CB) = I

Either way, you can't "divide" by B in the first step. Amirite?


"divide" = multiply by B^(-1).

But yeah, you're not allowed to do that. You can either pre or post multiply. Not randomly shove it in in the middle.
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jpepsred
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Thanks for the help guys.

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