Curriculum placement

Precalculus. This describes the skill, not a learner estimate.

Which matrix rules hold

Demonstrate matrix noncommutativity and justify associative and distributive operations

Problem types

  • Matrix products and laws

Builds on

Leads to

  • Inverse of a matrix · Extend the idea

    Since order matters in a product, an inverse must satisfy both AA^-1 = I and A^-1A = I, and the identity matrix is the matrix that leaves a product unchanged.

  • Matrices as transformations of the plane · See it applied

    Matrix laws such as order of multiplication decide how a sequence of transformations composes.

Related skills

  • Composition of functions · Related idea

    Matrix multiplication and function composition both depend on order: AB differs from BA, and f of g differs from g of f.

  • Which number systems stay closed · Related idea

    Closure and properties are checked for matrices as for numbers: matrices add and multiply, but multiplication is not commutative.

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