Question about Multiplying Matrices

[deana]

If I reduce two matrices using row operations before multiplying them together, will I still get a row-equivalent answer to the result I would of gotten if I hadn't reduced them?

Thanks for any input!

 

[Bohrok]

In short, no. If we look at multiplying two 2x2 matrices, row reducing them first would leave 0 in the bottom left entry in each one, and their product will have a 0 in that entry as well. (This would be an example of two upper triangular matrices being multiplied, and their product will always be upper triangular too.) But not every product of 2x2 matrices will have a 0 in the bottom left corner, so in general, row reducing them first won't give you a row-equivalent answer.