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

Show that the nxn matrix A is invertible iff its determinant is non-zero.

I think I can do this, but would like the validity checked.

2. Relevant equations

I would use |A| = the product of diagonal entries, because I don't know how to prove the non-diagonal entries of zero for [tex]A{C^T} =|A|I[/tex], where C is the cofactor matrix.(shown on Gil's videos)

[tex]AA^{-1}=I[/tex]

3. The attempt at a solution

Using eliminationto show A in rref, That is, all non diagonal entries of zero, then the det is the product of diagonals. If det=0 then at least one entry of diagonals (a11,a22,...,ann) = 0. Then this 0('s) entry cannot be multiplied to produce the entry in the identity matrix needed for [tex]AA^{-1}=I[/tex]

Is this ok?, if not , some direction would be most appreciated.

DIM

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# Homework Help: Proof on invertible matrices

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