question_answer

Find the additive inverse of the matrix \[A=\left[ \begin{matrix}    2 & -\,5 & 0  \\    4 & 3 & -\,1  \\ \end{matrix} \right]\]

Answer:

Clearly, the additive inverse of the given matrix A is the matrix \[(-\,A),\]given by \[-\,A=\left[ \begin{align}   & \begin{matrix}    -\,2 & -\,(-\,5) & 0  \\ \end{matrix} \\  & \begin{matrix}    -\,4 & \,\,\,\,\,-\,3 & -\,(-\,1)  \\ \end{matrix} \\ \end{align} \right]=\left[ \begin{align}   & \begin{matrix}    -\,2 & \,\,\,\,5 & 0  \\ \end{matrix} \\  & \begin{matrix}    -\,4 & -\,3 & 1  \\ \end{matrix} \\ \end{align} \right]\]