I have a compute a calculus with a negative power on a matrix, however, due of my low math level, I am not sure on how powers and moreover negative ones applies on matrices could you give me some advices ? this calculus is this one: 
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4That $-1$ means the inverse of the matrix. I hope you know enough about $2 \times 2$ matrices to compute the inverse. – Ethan Bolker Oct 04 '16 at 12:36
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ho ok. thanks you ! – Gabrielle de Grimouard Oct 04 '16 at 12:45
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Yes, $A^{-n}$ is the inverse matrix to $A^n$ or, equivalently, the nth power of $A^{-1}$. Of course, A must be invertible for that to exist. – user247327 Oct 04 '16 at 12:45
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Given a square matrix $A$, $A^{-1}$ is the inverse of A, that exists iff $\det A \ne0$.
For $2\times2$ matrix it is: $$ \begin{bmatrix} a&b\\c&d \end{bmatrix}^{-1}= \begin{bmatrix} d&-b\\-c&a \end{bmatrix}\frac{1}{\det A} $$
Emilio Novati
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