Question

Can Cramer’s rule be used to solve the system A[x] [0]
[ y] =[0]
[ z] [a]
Where A is given and ais not equal to zero

Answer 1

If here the system is $A[x]=[0]$ then using the Cramer's rule we will obtain only trivial solution $[x]=[0]$ in case if $detA\ne 0$. Otherwise we can't apply the Cramer's rule to this system