Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Inverse of a matrix
Use identity matrices and determinants to determine and compute inverses
Problem types
- Determinants and 2×2 inverses
Builds on
- Operations on matrices
- Which matrix rules hold · Earlier 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.
Leads to
- A system written as a matrix equation
- Matrices as transformations of the plane · See it applied
The inverse of a transformation matrix undoes the transformation.
Related skills
- Finding an inverse function · Related idea
An inverse function undoes a function, as an inverse matrix undoes the matrix transformation.
- What a transformation keeps · Related idea
The inverse of a rigid motion is a rigid motion, and its matrix undoes the original matrix, so invariants such as length are preserved by both.
- Why elimination keeps the same solutions · Related idea
Elimination steps that keep a system equivalent are the row operations used to find an inverse matrix.
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