Question

Find the product, if possible of : $\left[\begin{array}{ccc}o&c&-b\\-c&0&a\\b&-a&0\end{array}\right] \left[\begin{array}{ccc}a^{2}&ab&ac\\ab&b^{2}&bc\\ac&bc&c^{2}\end{array}\right]$

Answer 1

Answer:

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

Step-by-step explanation:

$\left[\begin{array}{ccc}0&c&-b\\-c&0&a\\b&-a&0\end{array}\right] \left[\begin{array}{ccc}a^{2}&ab&ac\\ab&b^{2}&bc\\ac&bc&c^{2}\end{array}\right]$

$\left[\begin{array}{ccc}0\times a^2 + c \times ab + (-b) \times ac&0 \times ab + c \times b^2 + (-b) \times bc& 0 \times ab + c \times bc + (-b) \times c^2\\-c \times a^2 + 0 \times ab + a \times ac&-c \times ab + 0 \times b^2 + a \times bc&-c \times ac + 0 \times bc + a\times c^2\\b\times a^2+(-a)\times ab+0 \times ac &b\times ab+(-a)\times b^2+0\times bc&b\times ac+(-a)\times bc+0\times c^2\end{array}\right]$

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