Question
If the inverse of $A^{2}$ is $B$, show that the inverse of $A$ is $A B$. (Thus $A$ is invertible whenever $A^{2}$ is invertible.)
Step 1
This means that $A^{2}B = I$, where $I$ is the identity matrix. Show more…
Show all steps
Your feedback will help us improve your experience
Sirat Shah and 88 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $A$ and $B$ are invertible, check that $B^{-1} A^{-1}$ is the inverse of $A B$.
Matrix Algebra and Applications
Matrix Inversion
Show that if $A B$ is invertible, so is $B$
Matrix Algebra
Characterizations of Invertible Matrices
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD