Chapter 4 - Vector Spaces - 4.2 Vector Spaces - 4.2 Exercises - Page 160: 12

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

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