(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If A is an invertible idempotent matrix, then A must be the Identity matrix I_n.

2. Relevant equations

A^2==A ; A^2==AA; A^(-1); I==A^(-1)

3. The attempt at a solution

Suppose A is an nxn matrix =/= I_n.

s.t. A^(2)==A

so A^(2)==A ==> AA==A

==> A^(-1)AA==A^(-1)A ==> A==I==> A^(-1)A==A^(-1)I==>I==A^(-1)I==A^(-1)==A

which yeilds a contradiction because we supposed our A =/= I_n.

Therefore A==I_n

Is this correct please help me understand where I have failed...

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# Homework Help: Linear algebra proof.

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