Question 1
The trace of a singular 
Explanation: 
, being a singular matrix, must have 0 as an eigenvalue; it also has 
as an eigenvalue. Being 
, it will have one more; call this eigenvalue 
.
The sum of the eigenvalues of a matrix is equal to its trace, so
The set of eigenvalues is 
. The eigenvalues of a matrix are the solutions of its characteristic (polynomial) equation, which, as a consequence, is
, being a singular matrix, must have 0 as an eigenvalue; it also has as an eigenvalue. Being , it will have one more; call this eigenvalue .
The sum of the eigenvalues of a matrix is equal to its trace, so
The set of eigenvalues is . The eigenvalues of a matrix are the solutions of its characteristic (polynomial) equation, which, as a consequence, is