Question

Find the product, if possible of : $\left[\begin{array}{ccc}2&2&1\\1&0&2\\2&1&2\end{array}\right] \left[\begin{array}{ccc}-2&-3&4\\2&2&-3\\1&2&-2\end{array}\right]$

Answer 1

Answer:

$\left[\begin{array}{ccc}1&0&0 \\0&1 &0\\0&0&1\end{array}\right]$

Step-by-step explanation:

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

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

$= \left[\begin{array}{ccc}1&0&0 \\0&1 &0\\0&0&1\end{array}\right]$