Since are invertible matrix, so we can say that
${\left(\mathit{A}\mathit{B}\right)}^{-1}={\mathit{B}}^{-1}{\mathit{A}}^{-1}$
Also, ${\mathit{A}}^{-1}=1\left|\mathit{A}\right|\left(\frac{\mathrm{adj}}{\mathit{A}}\right)$
$\Rightarrow \mathrm{adj}\left(\mathit{A}\right)=|\mathit{A}|\cdot {\mathit{A}}^{-1}$
$\left|{\mathit{A}}^{-1}\right|=\frac{1}{\left|\mathit{A}\right|}$
$\left|{\mathit{A}}^{-1}\right|=|\mathit{A}{|}^{-1}$
Now, ${\left(\mathit{A}+\mathit{B}\right)}^{-1}=\frac{1}{\left|\left(\mathit{A}+\mathit{B}\right)\right|}\mathrm{adj}\left(\mathit{A}+\mathit{B}\right)$
$\Rightarrow {\left(\mathit{A}+\mathit{B}\right)}^{-1}\ne {\mathit{A}}^{-1}+{\mathit{B}}^{-1}$
This statement is not true. The inverse of a sum of matrices is not equal to the sum of their inverse.