[tex]-2\mathbf A+3\mathbf I=\mathbf0[/tex]
[tex]\implies \mathbf A=\dfrac32\mathbf I[/tex]
[tex]\implies \mathbf A+\mathbf I=\dfrac52\mathbf I[/tex]
[tex]\implies \det(\mathbf A+\mathbf I)=\det\left(\dfrac52\mathbf I\right)=\left(\dfrac52\right)^3\det\mathbf I=\dfrac{125}8[/tex]
