Let A=(0100)A = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}A=(0010). Compute A3A^3A3.
(0000)\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}(0000)
(0100)\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}(0010)
(0010)\begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}(0100)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)