$ \left\{ \begin{bmatrix} x & x \\ x & x \end{bmatrix} \, \big| \, x \text{ is a nonzero real number} \right\} $ is a group with respect to matrix multiplication. In this group, the inverse of $ \begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix} $ is ...

Question

$ \begin{bmatrix} \frac{4}{3} & \frac{4}{3} \\ \frac{4}{3} & \frac{4}{3} \end{bmatrix} $

$ \begin{bmatrix} \frac{3}{4} & \frac{3}{4} \\ \frac{3}{4} & \frac{3}{4} \end{bmatrix} $

$ \begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix} $

$ \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} $

Solution

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