- #1

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My Try:

AB = BC

A^-1 AB = A^-1 BC

IB = A^-1BC

Also why does B = C not contradict the statement that "the cancellation law doesn't hold for matrices"?

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- Thread starter ha9981
- Start date

- #1

- 32

- 0

My Try:

AB = BC

A^-1 AB = A^-1 BC

IB = A^-1BC

Also why does B = C not contradict the statement that "the cancellation law doesn't hold for matrices"?

- #2

HallsofIvy

Science Advisor

Homework Helper

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Surely, that's not what you want to prove? It's not true. Take A= C and then, for any B, AB= BC because both are just AB.

You must have meant "If AB= AC then B= C". Just multiply both sides on the left by A[sup[-1[/sup].

And it does not contradict the statement "the cancellation law doesn't hold for matrices" because the cancellation law says that "If AB= AC for any non-zero A, then B= C". The theorem you are trying to prove requires that A be invertible. There are many non-zero matrices that are not invertible.

You must have meant "If AB= AC then B= C". Just multiply both sides on the left by A[sup[-1[/sup].

And it does not contradict the statement "the cancellation law doesn't hold for matrices" because the cancellation law says that "If AB= AC for any non-zero A, then B= C". The theorem you are trying to prove requires that A be invertible. There are many non-zero matrices that are not invertible.

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