If the Determinant is 0, what all is true? matrices fun

[mr_coffee]

Hello everyone I'm stuck on this problem, how its wrong, i got parts a and c, but b i can't get. Hre is what it says:

Consider the following general matrix equation:
[a1 a2] =
|m11 m12| * [x1 x2]
|m21 m22|

which can also be written as A = MX
Determinant of M = m11m22 - m12m21

A. given any X there is one and only one A which will satisfy the equation.
B. given any A there is one and only one X which will satisfy the equation.
C. there is no value of Xwhich satisfies the equation when A =0 .
D. some values of A will have no values of X which will satisfy the equation.
E. some values of A (such as A=0) will allow more than one X to satisfy the equation.

I said for sure A, and B are wrong because they are what happens if Det(M) is not equal to 0. so it has to be a combination of C,D, and E.

I tried like all combinations of C,D,and E, and nothing works!

 

[CarlB]

I said for sure A, and B are wrong ...

You might go over your logic behind why you think that A is wrong.

Carl