1. use approach AX=$\lambda$X where A Will be the matrix present in ans options and as eigen values (lamda) is known, the matrix which satisfies is your ans
2. follow the same approach as above AX=$\lambda$X OR MATRIX WILL BE sufficient to find eigen values.
3. MANY ways actually the above approach(same) OR You can use Cramers rule, Substitution (after converting it into row echelon form and it is based on rank). if you need example please comment.
NOTE: X REPRESENTS EIGEN VECTOR
for example plzz https://gateoverflow.in/43968/isro-2013-33