Practice question · Match the pairs
Match each term to its meaning.
- The identity matrix I
- The inverse of A
- A singular matrix
- Undoing a composition
- The matrix that undoes what A did
- Reverse the last step first, then the one before
- Leaves every vector exactly where it was
- Collapses space, so nothing can undo it
Hints
- Two entries describe matrices, two describe rules for using them.
- One rule reverses an order and one solves a system.
Show the answer
- The identity matrix I → Leaves every vector exactly where it was
- The inverse of A → The matrix that undoes what A did
- A singular matrix → Collapses space, so nothing can undo it
- Undoing a composition → Reverse the last step first, then the one before
Why
The inverse undoes A, singular matrices cannot be undone, products invert in reverse order, and the inverse packages the solution of a linear system. In practice Gaussian elimination is faster for large systems, but the inverse is the cleanest way to see WHY the solution is unique.
Practise Matrix Inverses
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