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# FP1 Matrices question Watch

1. 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.
2. (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.

And premultiply by C inverse, and then by A inverse.
3. (Original post by ghostwalker)
You made an error in going from the first quoted line to the second.

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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