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I'm trying to understand the reason why $A$ is invertible only if $\mathrm{adj}\,A$ is invertible.

That's what I have right now: $A\, \mathrm{adj}\,A = |A|\cdot I$.

So if we take $\det$ of both sides we get: $|A\,\mathrm{adj}\,A| = ||A|\cdot I|$

and then: $|A| \cdot |\mathrm{adj}\,A| = |A|^n$

but now I'm stuck...

Appreciate your help.

  • 4
    Is $A$ a $5\times 5$ matrix?2012-10-13
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    What is $\mathrm{adj} A$?2012-10-13
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    @Norbert http://en.wikipedia.org/wiki/Adjugate_matrix2012-10-13
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    @anon thanks!${}$2012-10-13

2 Answers 2