Inverse of [[4,7],[2,6]]: animated lesson

1. 1. The problem
   Worked example

   $\begin{bmatrix}4 & 7 \\ 2 & 6\end{bmatrix}^{-1}$
2. 2. Step by step
   1. $$\det A = 10 \neq 0$$
      Check that the determinant is non-zero
   2. $$A^{-1} = \frac{1}{10}\begin{bmatrix}6 & -7 \\ -2 & 4\end{bmatrix} = \begin{bmatrix}\frac{3}{5} & -\frac{7}{10} \\ -\frac{1}{5} & \frac{2}{5}\end{bmatrix}$$
      Swap a and d, negate b and c, divide by the determinant
   3. $$A A^{-1} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$
      Check: A·A⁻¹ = I
3. 3. The answer
   $$A^{-1} = \begin{bmatrix}\frac{3}{5} & -\frac{7}{10} \\ -\frac{1}{5} & \frac{2}{5}\end{bmatrix}$$

   A⁻¹ = [[3/5, -7/10], [-1/5, 2/5]]

4. 4. Check
   • ✓Multiplying A by the result gives the identity matrix exactly.

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