A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0
apply cayley Hamilton theorem . replace A with lamda and equate to 0.
then solve .
you will get lamda1 = 0 ,lamda2= 0 and lamda3 = 2.
If we apply the cayley hamilton theorum, the Cayley–Hamilton theorem states that every square matrix satisfies its own characteristic equation.
so 2 is one of the possible value for eigen values
And A is singular means that its determinant is 0