Multiply [[2,1],[1,3]]^3: animated lesson

1. 1. The problem
   Worked example

   Aⁿ (power): A = [[2, 1], [1, 3]]
2. 2. Step by step
   1. $$A = \begin{bmatrix}2 & 1 \\ 1 & 3\end{bmatrix}\ (2×2)$$
      Read matrix A
   2. $$\begin{bmatrix}5 & 5 \\ 5 & 10\end{bmatrix}$$
      Multiply again: power 2
   3. $$\begin{bmatrix}15 & 20 \\ 20 & 35\end{bmatrix}$$
      Multiply again: power 3
   4. $$\begin{bmatrix}15 & 20 \\ 20 & 35\end{bmatrix}$$
      Result
3. 3. The answer
   $$\begin{bmatrix}15 & 20 \\ 20 & 35\end{bmatrix}$$

   [[15, 20], [20, 35]]

4. 4. Check
   • ✓All arithmetic is exact (fractions, no rounding).

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