Question

A is a 3x3 matrix and -2A +3I = 0. Enter det(A+I)

Answer 1

`-2\mathbf A+3\mathbf I=\mathbf0`

`\implies \mathbf A=\frac32\mathbf I`

`\implies \mathbf A+\mathbf I=\frac52\mathbf I`

`\implies \det(\mathbf A+\mathbf I)=\det\left(\frac52\mathbf I\right)=\left(\frac52\right)^3\det\mathbf I=\frac{125}8`