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For $A,B \in M^{3 \times 3}$, I want to prove the following property:

$det(A+B)=detA + <$Cof$A,B> + <A,$Cof$B> + detB$ where $<.,.>$ denotes the usual inner product on $M^{3\times3}$

Any help and suggestion would be appreciated.

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  • $\begingroup$ What do you mean by $Cof A$? And what ist "the usual inner product on $M^{3x3}$. Do you just identify $M^{3x3}$ with $M^{9}$? $\endgroup$
    – Takirion
    Mar 3, 2016 at 17:41
  • $\begingroup$ $M^{3 \times 3}$ means the set of the 3 by 3 matrices. Also Cof A means the cofactor of the matrix A @Takirion $\endgroup$
    – user189013
    Mar 3, 2016 at 19:13

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