If A=(0100)A = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}A=(0010), what is ATA^TAT?
(0010)\begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}(0100)
(0100)\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}(0010)
(1000)\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}(1000)
(0001)\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}(0001)