CCSS.Math.Content.HSN-VM.C.9
The standard
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
What this standard means
Students need to multiply square matrices and notice that order matters. They should be able to compute AB and BA, compare the results, and explain why they are usually different. They also need to use examples to show that grouping and distributing still work with matrices when the sizes fit.
Mastery looks like accurate matrix products and clear reasoning about order, grouping, and distribution. Students often get stuck treating matrices like regular numbers. They may also make arithmetic errors, mix up rows and columns, or assume one counterexample proves every case.
Ways to teach it
- Have students use 2 by 2 number cards to build matrices A and B, then calculate AB and BA side by side.
- Ask students to write: Why does changing the order in matrix multiplication change the result, but changing the grouping does not?
- Give one pair of 2 by 2 matrices and ask students to compute AB and BA on an exit ticket.
- Connect matrix order to transformations by rotating and reflecting a graph point in different orders, then comparing final coordinates.
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Related standards
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