MathematicsGeneralQuality 78 · Exceptional

Why Matrices Multiply the Way They Do

@author · 2026-06-25 · v1

7 min read

Matrix multiplication combines linear transformations. When you multiply

AB

, each row of

A

is paired with each column of

B

via dot products, producing a matrix that represents applying transformation

B

then

A

. The order matters because transformations generally don't commute.

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