Question

If A is a 3 ×3 matrix and 5(A+I)=I. What is det(A+I) .

Answer 1

`5(\mathbf A+\mathbf I)=\mathbf I\implies \mathbf A=-\frac45\mathbf I`

`\implies\det\mathbf A=\det\left(-\frac45\mathbf I\right)=\left(-\frac45\right)^3\det\mathbf I=-(64)/(125)`