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FP1 Matrices question

Hi I'm stuck on this question.

4a) Given that ABC = I, prove that B^-1 = CA - this part was fine
b) Given that A =

and C =

, find B

This is my working:
ABC = I
A^-1ABC = A^-1I
BC = A^-1
BCC^-1 = A^-1C^-1
B = (AC)^-1

However this gives a matrix which is wrong and the book wants me to do B = (CA)^-1 ; I cannot see how to get to this. Thanks for the help in advance.

Reply 1

ghostwalker

Original post by livg

BCC^-1 = A^-1C^-1
B = (AC)^-1

You made an error in going from the first quoted line to the second.

A^{-1}C^{-1}= (CA)^{-1}

To prove it, start with:

(CA)(CA)^{-1}=I

And premultiply by C inverse, and then by A inverse.

(edited 9 years ago)

Reply 2

livg

Original post by ghostwalker

You made an error in going from the first quoted line to the second.

A^{-1}C^{-1}= (CA)^{-1}

To prove it, start with:

(CA)(CA)^{-1}=I

And premultiply by C inverse, and then by A inverse.

Ah - I didn't realise you switched them! Makes sense though now - thank you.

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