3.5-02 Verifying an inverse

Verifying an inverse — linear algebra practice

Check proposed inverses through multiplication and distinguish transpose from inverse. Work with shears, rotations and rectangular one-sided identities, then prove inverse uniqueness. Rounded numerical products are treated as approximate evidence rather than exact algebraic proof.

What you will practise

• Verify inverse identities
• Recognize when transpose is inverse
• Handle one-sided and numerical qualifications

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review matrix products and invertibility. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to validate inverse calculations and claims.