Question

The order of $\left[\begin{array}{ccc}x& y& z\end{array}\right]\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$ is

• A. $3\times 1$
• B. $1\times 1$
• C. $1\times 3$
• D. $3\times 3$

Answer 1

Answer: (B)

$1\times 1$

Let $ABC=\left[\begin{array}{ccc}x& y& z\end{array}\right]\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$
Here,the order of $A$ is $1\times 3$
Order of $B$ is $3\times 3$
Order of $C$ is $3\times 1$
Since, matrix multiplication satisfies associative property
i.e. $\left(AB\right)C=A\left(BC\right)$
Hence, the order of $AB$ is $1\times 3$.
Hence, the order of $ABC$ is $1\times 1$.