Question

The additive inverse of the matrix $A=\left[\begin{array}{cc}3& -1\\ 2& 5\end{array}\right]$ is

• A. $\left[\begin{array}{cc}-3& 0\\ -2& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}-3& 1\\ -2& -5\end{array}\right]$
• C. $\left[\begin{array}{cc}3& 1\\ 5& 2\end{array}\right]$
• D. $\left[\begin{array}{cc}-3& 1\\ 2& -5\end{array}\right]$

Answer 1

Answer: (B)

The given matrix is $A=\left[\begin{array}{cc}3& -1\\ 2& 5\end{array}\right]$.
Then, its additive inverse is $-A$.
$\Rightarrow -A=(-1)A$ $-(-1)\left[\begin{array}{cc}3& -1\\ 2& 5\end{array}\right]-\left[\begin{array}{cc}-3& 1\\ -2& -5\end{array}\right]$