Question
Show that if $\mathbf{A}$ is a nonsingular matrix, then $\operatorname{det} \mathbf{A}^{-1}=1 /$ det $\mathbf{A}$.
Step 1
e., $\mathbf{A}\mathbf{A}^{-1} = \mathbf{I}$. Show more…
Show all steps
Your feedback will help us improve your experience
Hast Aggarwal and 72 other Algebra 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
Let $A$ be a nonsingular matrix. Show that $A^{-1}$ is also nonsingular and $\left(A^{-1}\right)^{-1}=A$
Matrices and Systems of Equations
Matrix Algebra
Prove that if $A$ is a square matrix, then $\operatorname{det}\left(A^{T} A\right)=\operatorname{det}\left(A A^{T}\right)$.
Determinants
Properties of Determinants; Cramerβs Rule
Verify that $\operatorname{det} \mathbf{A}=\operatorname{det} \mathbf{A}^{T}$ for the given matrix $\mathbf{A}$. $$ \mathbf{A}=\left(\begin{array}{rrr} 1 & 2 & 1 \\ 4 & 1 & -1 \\ 1 & 2 & -1 \end{array}\right) $$
Matrices
Properties of Determinants
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD