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Where to put the inverse matrix

Hello guys, I am currently revising FP1 and sometimes depending on how unlucky I am get the position on where to multiply the inverse matrix wrong.

Here is an example:

If both A B and C are 2x2 matrices and I have to find B:

AB=C should I do A-1AB=A-1C or AA-1A=CA-1


Plese enlighten because it is really annoying me as this could penalise me in the exams.
Original post by Craig David
Hello guys, I am currently revising FP1 and sometimes depending on how unlucky I am get the position on where to multiply the inverse matrix wrong.

Here is an example:

If both A B and C are 2x2 matrices and I have to find B:

AB=C should I do A-1AB=A-1C or AA-1A=CA-1


Plese enlighten because it is really annoying me as this could penalise me in the exams.

A1A=I,AA1=IA^{-1}A = I, A A^{-1} = I. Do whichever lets you simplify using those two rules, bearing in mind that you can say essentially nothing about ABA1=CA1ABA^{-1} = CA^{-1}.

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