Question

Let A be a square matrix of order 2 * 2 , then |kA|

Answer 1

Answer:

    |kA| = k²|A|

Step-by-step explanation:

As A is 2×2, it has the form

$\displaystyle A=\left(\begin{matrix}a&b\\c&d\end{matrix}\right)$

Then

$\displaystyle kA=\left(\begin{matrix}ka&kb\\kc&kd\end{matrix}\right)$

So

$\displaystyle|kA|=\left|\begin{matrix}ka&kb\\kc&kd\end{matrix}\right|=(ka)(kd)-(kb)(kc)=k^2(ad-bc)=k^2|A|$