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General question:

How do you determine a matrix B when given A and AB?

How do you determine a matrix B when given A and AB?

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- Thread starter fk378
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- #1

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General question:

How do you determine a matrix B when given A and AB?

How do you determine a matrix B when given A and AB?

- #2

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If you know the inverse of A, you can multiply on the left side by A^-1 to get B, i.e. (A^-1)AB = B.

- #3

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Oh I see. I understand the computation, but could you explain the theory behind this?

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- #5

HallsofIvy

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If you were given two

If A has an inverse, then A

Notice the condition "If A has an inverse". There are plenty of different matrices, A, B, not having inverses, such that AB= 0. If A does not have an inverse, there may be many different matrices B such that AB= C.

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