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Point of Inflection

If A=diag2,4,...

Question

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

A

\frac{19}{20}

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B

\frac{13}{20}

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C

11

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D

12

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Solution

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

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