Answer:
Yes, A4×4 04×4 = 04×4 A4×4 = 04×4
For some matrices AB = BA. But not in general.
Yes, A4×4 04×4 = 04×4 A4×4 = 04×4
For some matrices AB = BA. But not in general.
Usually people write A0 = 0A = 0 where it is assumed that the zero matrix has the correct dimensions to make the multiplication possible.
It would be good at this point to practice matrix multiplication. The goal is to internalize the idea so that it becomes one of your active concepts, not a faintly recalled notion you have to look up each time.
In the following, mentally (or on paper) multiply the two matrices. Click on the "=" button to check your answer. Change elements in A and B and work the problem again. To change an element, replace the contents of a cell and then click outside of the cell.
Try some interesting problems, such as:
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1 0 0 1 |
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1 2 3 4 |
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= |
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1 2 3 4 |
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1 0 0 1 |
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= |
Do you suspect that c(AB) = (cA)B for scalar (real number) c?