If A=(} -4&1&-4 3&3&1 2&5&5 ) find AB. a. C. (} 12&15&-17 -1&-4&-4 17&14&-22 ) (} 11&14&-17 -1&-4&-3 17&15&-22 ) b. d. (} 11&15&-17 -1&-3&-4 16&15&-22 ) (} 11&15&-17 -1&-4&-4 17&15&-22 )

To find the product of matrices A and B, we need to multiply each element of the rows of matrix A with the corresponding element of the columns of matrix B and sum up the products.<br /><br />Let's calculate the product AB:<br /><br />AB = $(\begin{matrix} -4&1&-4\\ 3&3&1\\ 2&5&5\end{matrix} )$ * $(\begin{matrix} -4&-5&4\\ 3&3&-5\\ 2&2&-1\end{matrix} )$<br /><br />AB = $(\begin{matrix} (-4*-4+1*3+-4*2)&(-4*-5+1*3+-4*-1)&(-4*4+1*-5+-4*-1)\\ (3*-4+3*3+1*2)&(3*-5+3*3+1*-1)&(3*4+3*-5+1*-1)\\ (2*-4+5*3+5*2)&(2*-5+5*3+5*-1)&(2*4+5*-5+5*-1)\end{matrix} )$<br /><br />AB = $(\begin{matrix} 16+3-8&20+3+4&-16-5+4\\ -12+9+2&-15+9-1&12-15-1\\ -8+15+10&-10+15-5&8-25-5\end{matrix} )$<br /><br />AB = $(\begin{matrix} 11&15&-17\\ -1&-4&-4\\ 17&15&-22\end{matrix} )$<br /><br />Therefore, the correct answer is option b.