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# FP1 Matrices question

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1. Why is that in this question (part c) http://i.imgur.com/1o1uiPl.png
BA=C is changed to B=CA^(-1)

While in this question http://i.imgur.com/bH4ZwNV.png
MC =A is changed to C=M^(-1)A (from the markschemes)

When should the inverse thats being multiplied through be on the left or right.

Thanks
2. (Original post by Ruhal)
Why is that in this question (part c) http://i.imgur.com/1o1uiPl.png
BA=C is changed to B=CA^(-1)

While in this question http://i.imgur.com/bH4ZwNV.png
MC =A is changed to C=M^(-1)A (from the markschemes)

When should the inverse thats being multiplied through be on the left or right.

Thanks
Two things:

1) What you do to one side of the equation you must do to the other to maintain equality.

2) Matrix multiplication is not commutative, in general, .

So, If BA=C

To get rid of the A, we have to post multiply by A^-1.

and do the same to the other side of the equation.

If you'd premultiplied by A^-1, you'd end up with:

which is not what you want.

A similar argument for the other case.
3. (Original post by ghostwalker)
Two things:

1) What you do to one side of the equation you must do to the other to maintain equality.

2) Matrix multiplication is not commutative, in general, .

So, If BA=C

To get rid of the A, we have to post multiply by A^-1.

and do the same to the other side of the equation.

If you'd premultiplied by A^-1, you'd end up with:

which is not what you want.

A similar argument for the other case.

Thanks a bunch!

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