Question

$\left[\begin{array}{ccc}1& -1& 2\\ 0& 2& -3\\ 3& -2& 4\end{array}\right]\left[\begin{array}{ccc}-2& 0& 1\\ 9& 2& -3\\ 6& 1& -2\end{array}\right]$

Answer 1

$\left[\begin{array}{ccc}1& -1& 2\\ 0& 2& -3\\ 3& -2& 4\end{array}\right]\left[\begin{array}{ccc}-2& 0& 1\\ 9& 2& -3\\ 6& 1& -2\end{array}\right]$

$\left(\begin{array}{ccc}1& -1& 2\end{array}\right)\left(\begin{array}{c}-2\\ 9\\ 6\end{array}\right)=1\cdot (-2)+(-1)\cdot 9+2\cdot 6$

$\left(\begin{array}{ccc}1& -1& 2\end{array}\right)\left(\begin{array}{c}0\\ 2\\ 1\end{array}\right)=1\cdot 0+(-1)\cdot 2+2\cdot 1$

$\left(\begin{array}{ccc}1& -1& 2\end{array}\right)\left(\begin{array}{c}1\\ -3\\ -2\end{array}\right)=1\cdot 1+(-1)(-3)+2(-2)$

$\left(\begin{array}{ccc}0& 2& -3\end{array}\right)\left(\begin{array}{c}-2\\ 9\\ 6\end{array}\right)=0\cdot (-2)+2\cdot 9+(-3)\cdot 6$

$\left(\begin{array}{ccc}0& 2& -3\end{array}\right)\left(\begin{array}{c}0\\ 2\\ 1\end{array}\right)=0\cdot 0+2\cdot 2+(-3)\cdot 1$

$\left(\begin{array}{ccc}0& 2& -3\end{array}\right)\left(\begin{array}{c}1\\ -3\\ -2\end{array}\right)=0\cdot 1+2(-3)+(-3)(-2)$

$\left(\begin{array}{ccc}3& -2& 4\end{array}\right)\left(\begin{array}{c}-2\\ 9\\ 6\end{array}\right)=3(-2)+(-2)\cdot 9+4\cdot 6$

$\left(\begin{array}{ccc}3& -2& 4\end{array}\right)\left(\begin{array}{c}0\\ 2\\ 1\end{array}\right)=3\cdot 0+(-2)\cdot 2+4\cdot 1$

$=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$