Mathematics - Matrices Question with Solution | TestHub

Since $\det (\mathrm{A})=2,\mathrm{adj}\left(A^2\right)=\det \left(A^2\right){\left(A^2\right)}^{-1}=4{\left(A^2\right)}^{-1}$. Hence $A^3\mathrm{adj}\left(A^2\right)=4A$, and its trace is $4(1+2+3)=24$.