Question

Let A be a 3 x 3 matrix such that A^2 = 2A. Prove that det(A) must be either 0 or 8.

Answer 1

As per the given question,

$A^2=2A$

So, $A^2-2A=0$

$A(A-2I)=0$

So, A=0 or A=2I

As we know, $A^2=2A$ is possible only for the diagonal matrix.

Here the given matrix is order of 3x3

So, det(A)=0 or det(A)=8