Coupled inductor question

[Learner]

coupled inductor equation

Hi everyone,
I was wondering if someone could help me figure the state space equation for this circuit, according to the coupled inductor equation

V1 =  L1 di1/dt   -   M di2/dt
V2 = -M di1/dt    +   L2 di2/dt

which gives me 

V1 =   1  di1/dt   -     1/2 di2/dt
V2 = -1/2 di1/dt   +     1/4 di2/dt

matrix form 

V1 =  1     -1/2   | di1/dt |
V2 = -1/2    1/4   | di2/dt |

then I have 

| di1/dt | = |  1     -1/2  |(inverse)   |V1| 
| di2/dt | = | -1/2    1/4  |            |V2|

equals to

| di1/dt | = |  1/4   1/2  |   |V1| 
| di2/dt | = |  1/2     1  |   |V2|
               ____________
                 1/4 - 1/4

I am getting 0 at the denominator, can anyone tell me what I am doing wrong?

Thanks in advance!