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\end{equation}  which means for this particular instance, matrix multiplication has become matrix addition. (However, this rule also does not appear to generally hold).  The above matrix resembles another matrix which when squared is twice itself \begin{equation}  \begin{bmatrix}  1&0&0&1\\0&1&1&0\\0&1&1&0\\1&0&0&1  \end{bmatrix}  \cdot  \begin{bmatrix}  1&0&0&1\\0&1&1&0\\0&1&1&0\\1&0&0&1  \end{bmatrix}  =  \begin{bmatrix}  2&0&0&2\\0&2&2&0\\0&2&2&0\\2&0&0&2  \end{bmatrix}  \end{equation}  This matrix is also an invariant under the transform $T$, whereas the first is not!