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Linear Algebra

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Inverse of Diagonal Factorization

LINALG-PRLRUC

Suppose that $A$ is a matrix and:

$$A=P \times D \times P^{-1}$$

...where:

$$D=\left [ \matrix {2 & 0\cr 0 & 5}\right ]$$

...and $P$ is a $2 \times 2 $ invertible matrix.

Which of the following would be equal to $A^{-1}$? Select ALL that apply.

A

$A^{-1}= P^{-1}\times D^{-1}\times P$

B

$A^{-1}=P \times D^{-1} \times P^{-1}$

C

$A^{-1}=P\times \left [ \matrix { 1/2 & 0 \cr 0 & 1/5}\right ] \times P^{-1}$

D

$A^{-1}=P^{-1} \times \left [ \matrix { 1/2 & 0 \cr 0 & 1/5}\right ] \times P$

E

None of the above.