Question

If $A=\text{diag}(2,4,5),$ then the trace of $A^{-1}$ is

• A. $\frac{19}{20}$
• B. $\frac{13}{20}$
• C. $11$
• D. $12$

Answer 1

The correct option is A $\frac{19}{20}$

Given $A$ is a diagonal matrix
$\therefore A^{-1}=\text{diag}(2^{-1},4^{-1},5^{-1})$
$\Rightarrow$ Trace of $A^{-1}=\frac{1}{2}+\frac{1}{4}+\frac{1}{5}=\frac{19}{20}$