Question

$(-A{)}^{-1}$ is always equal to: (where $A$ is a $n^{th}$ order invertible square matrix)

• A. $0$
• B. $-A^{-1}$
• C. $A^T$
• D. $A^{-1}$

Answer 1

The correct option is B $-A^{-1}$

$(-A{)}^{-1}=\frac{adj(-A)}{|-A|}=\frac{(-1{)}^{n-1}adj(A)}{(-1{)}^n|A|}=-\frac{adj\left(A\right)}{|A|}=-A^{-1}$