Chapter 4 - Vector Spaces - 4.2 Vector Spaces - 4.2 Exercises - Page 160: 9

$\left[\begin{array}{lll}{-a} & {-b} & {-c} \\ {-d} & {-e} & {-f} \end{array}\right]$

The additive inverse of any matrix $\left[\begin{array}{lll}{a} & {b} & {c} \\ {d} & {e} & {f} \end{array}\right]\in M_{2,3}$ is given by $$-\left[\begin{array}{lll}{a} & {b} & {c} \\ {d} & {e} & {f} \end{array}\right]=\left[\begin{array}{lll}{-a} & {-b} & {-c} \\ {-d} & {-e} & {-f} \end{array}\right].$$