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Matrix Power Calculator
Raise a matrix to an integer power step by step
The calculator will find the given matrix raised to the given integer (positive or negative) power (if possible), with steps shown. Thus, it can square and cube the matrix. It handles matrices of any size up to 7x7 (2x2, 3x3, 4x4, etc.).
Your Input
Find $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]^{2}$$$.
Solution
To raise a matrix to the power of $$$n$$$, multiply the matrix by itself $$$n - 1$$$ times.
$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]^{2} = \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right] = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$ (for steps, see matrix multiplication calculator).
Answer
$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]^{2} = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$A