Question 1021827
For a (square) homogeneous system of linear equations to have non-trivial solutions, the determinant of coefficients

{{{det(matrix( 2, 2, 
   a, 3,
   2, a+1
 )) = 0}}}

==>{{{a(a+1) - 6 = 0}}}, or {{{a^2 + a - 6 = 0}}} ==> (a+3)(a-2) = 0

==> a = -3 or 2.

So your answers are correct.