Question

If $3p=\left[\begin{array}{cc}6& 0\\ -9& 12\end{array}\right]$, then the matrix $2p$ is

• A. $\left[\begin{array}{cc}4& -6\\ 0& 8\end{array}\right]$
• B. $\left[\begin{array}{cc}12& 0\\ -18& 24\end{array}\right]$
• C. $\left[\begin{array}{cc}12& -18\\ 0& 24\end{array}\right]$
• D. $\left[\begin{array}{cc}4& 0\\ -6& 8\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}4& 0\\ -6& 8\end{array}\right]$

Given : $3p=\left[\begin{array}{cc}6& 0\\ -9& 12\end{array}\right]$

$⟹$ $p=\frac{1}{3}\left[\begin{array}{cc}6& 0\\ -9& 12\end{array}\right]$

$⟹$ $p=\left[\begin{array}{cc}2& 0\\ -3& 4\end{array}\right]$

$⟹$ $2p=2\left[\begin{array}{cc}2& 0\\ -3& 4\end{array}\right]$

$\therefore$ $2p=\left[\begin{array}{cc}4& 0\\ -6& 8\end{array}\right]$