Mathematics - Matrix Question with Solution | TestHub

Let $\mathrm{a}\in \mathbf{R}$ and A be a matrix of order $3\times 3$ such that $\det (A)=-4$ and $A+I=\left[\begin{array}{lll}1& a& 1\\ 2& 1& 0\\ a& 1& 2\end{array}\right]$, where $I$ is the identity matrix of order $3\times 3$.
If $\det ((a+1)\mathrm{adj}((a-1)A))$ is $2^m{3}^n,m,n\in$ $\{0,1,2,\dots .20\}$, then $\mathrm{m}+\mathrm{n}$ is equal to :