Question

A is a 2 ×2 matrix and 3(A+I)=I. Enter det(A+I).

Answer 1

$3(\mathbf A+\mathbf I)=\mathbf I$
$\mathbf A+\mathbf I=\dfrac13\mathbf I$
$\implies \det(\mathbf A+I)=\det\left(\dfrac13\mathbf I\right)=\left(\dfrac13\right)^2=\dfrac19$