Proof of $det(A+B)=detA + <$Cof$A,B> + <A,$Cof$B> + detB$

Question

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.