Question
Prove that if $c \neq 0$ is any nonzero scalar and $A$ is an invertible matrix, then the scalar product matrix $c A$ is invertible, and $(c A)^{-1}=\frac{1}{c} A^{-1}$.
Step 1
A matrix $A$ is invertible if there exists a matrix $B$ such that $AB = BA = I$, where $I$ is the identity matrix. We are given that $A$ is invertible, so there exists a matrix $A^{-1}$ such that $AA^{-1} = A^{-1}A = I$. Show more…
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