Question

Linear Algebra: Matricies with negative exponents:

Let A be a matrix.
Does A^(-x) = [A^(-1)]^(x) ?

Answer 1

\[A = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right], A^{-2}=(A^{-1})^{2} \]
In other words, is this true

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @mhchen
\[A = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right], A^{-2}=(A^{-1})^{2} = (A^{-1})*(A^{-1})\]
In other words, is this true
\(\color{#0cbb34}{\text{End of Quote}}\)