Which of these matrices is singular?

The Eigenvalues of are 

Given

Matrix multiplication is not defined for

The solution of the simultaneous equations

is

Four sets of simultaneous linear equations are shown in the table below.

The number of these sets of equations that have a unique solution is

Augmented matrix   is an example of inconsistent system.

The system of equations

Linear system has unique solution when

The solutions to Linear system  is 

Linear system inconsistent  when