If A=(1302)A = \begin{pmatrix} 1 & 3 \\ 0 & 2 \end{pmatrix}A=(1032), what is the product AIAIAI where III is the 2×22 \times 22×2 identity matrix?
(0000)\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}(0000)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)
(1302)\begin{pmatrix} 1 & 3 \\ 0 & 2 \end{pmatrix}(1032)
(2604)\begin{pmatrix} 2 & 6 \\ 0 & 4 \end{pmatrix}(2064)