Multiplying row exchange matrices

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SUMMARY

The discussion focuses on the multiplication of row exchange matrices, specifically the matrices p and q defined as p = [[0, 1, 0], [1, 0, 0], [0, 0, 1]] and q = [[0, 0, 1], [0, 1, 0], [1, 0, 0]]. The correct multiplication order is pq qp and p^2, leading to the resulting matrix [[0, 1, 0], [0, 0, 1], [1, 0, 0]]. A participant expresses confusion about the multiplication process, mistakenly believing they should multiply rows by columns, which resulted in a zero matrix. This highlights a common misunderstanding in matrix multiplication.

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  • Understanding of matrix multiplication rules
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Arnoldjavs3
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Homework Statement


Multiply these row excahnge matrices in the order pq qp and p^2
p =
[0 1 0]
[1 0 0]
[0 0 1]

q=
[0 0 1]
[0 1 0]
[1 0 0]

Homework Equations

The Attempt at a Solution


I don't understand why the solution is
[0 1 0]
[0 0 1]
[1 0 0]

do you not multiply rows by columns? When i do this i just get a 3x3 with 0s in the entire matrix. I don't understand, what am I doing wrong? Since this is a fundamental misunderstanding from my part.
 
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