If \( \mathrm{A}= \) diagonal \( \left[a_{1}, a_{2}, a_{3}\right], a_{i} \neq 0 \), then prove t...

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If \( \mathrm{A}= \) diagonal \( \left[a_{1}, a_{2}, a_{3}\right], a_{i} \neq 0 \), then prove that \( \mathrm{A}^{-1}= \) diagonal \( \left[a_{1}^{-1}, a_{2}^{-1}, a_{3}^{-1}\right] \).
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