Professor Justin Bieber has observed that only five multiplications are neededto compute the square of a $2\backslash$times $2$ matrix:abab a$2+$bcb$($a$+$d$)$c d c d $=$ c$($a$+$d$)$ bc$+$d$2$Professor Bieber remembers Strassens algorithm from COMP $3804.$ Based on this, he claims that, for any given n $\backslash$times n matrix A$,$ the matrix A$2=$ AA can be computed by a divide$-$and$-$ conquer algorithm that makes five recursive calls, resulting in a running time of O$($nlog $5).$