Why LTspice is showing singular matrix error in the following inverter circuit?
As Sphero says, there is no negative supply on U4 and U6.

Furthermore, 


The bottom of L1 must NOT be grounded, because activating M3 creates a dead short from Vcc, and M4 does nothing.
You are supplying signal for U3 and U4 from a ground reference, which will be significantly offset from U3/U4 supply references. (Research isolated MOSFET drivers.)
Also note a magnetic coupling coefficient of 0.0428 is extremely low. To quote this article,



  Leakage inductance can cause undesired voltage spikes or ringing which can lead to a requirement for snubbing circuits and their associated energy losses.
  For an initial simulation, it’s easier and often sufficient to ignore leakage inductance by setting the mutual coupling coefficient to 1.


Also,


  You may want to simulate the effects of leakage inductance in order to  consider snubber designs or work out the commutation timing of a resonantly
  switched converter. There are two ways to add leakage inductance to your model. You can either put extra inductors in series with the leads of the winding inductors — a very direct approach — or use a mutual coupling coefficient of less than one. The leakage inductance, \$L_{LEAK}\$, can be related to the
  winding inductance \$L\$ and coupling coefficient \$K\$ by the equation:
  \$L_{LEAK} = L \cdot (1 – K^2)\$. If K is close to 1, the two methods
  are electrically equivalent.