Numpy and inverse matrices - method to do only one reshape instruction - python-2.7

Question

I am doing a batch execution of high number of 3x3 matrices with CUDA.
The goal is to get a big matrix of 3x3 matrix (so I use a 4D array).
I have done previously the same operation with numpy.linalg.inv function. With this way, I can directly get an array of 3x3 matrix : I show you the code that performs this operation.
Now, with CUDA version, I would like to reshape in a minimum of instructions the big 1D array produced : so I have to build a (N,N,3,3) array from a (NN3*3) 1D array.
For the moment, I can do this reshape into 2 steps (here the code below).
The original version with classical numpy.linalg.inv is carried out by:
for r_p in range(N):
for s_p in range(N):
# original version (without GPU)
invCrossMatrix[:,:,r_p,s_p] = np.linalg.inv(arrayFullCross_vec[:,:,r_p,s_p])
invCrossMatrix represents a (3,3,N,N) array and I get it directly from the (3,3,N,N) arrayFullCross array (dimBlocks = 3)
For the moment, when I use GPU batch execution, I start from the 1D array :
# Declaration of inverse cross matrix
invCrossMatrix_temp = np.zeros((N**2,3,3))
# Create arrayFullCross_vec array
arrayFullCross_vec = np.zeros((3,3,N,N))
# Create arrayFullCross_vec array
invCrossMatrix_gpu = np.zeros((3*3*(N**2)))
# Build observables covariance matrix
arrayFullCross_vec = buildObsCovarianceMatrix3_vec(k_ref, mu_ref, ir)
## Performing batch inversion 3x3 :
invCrossMatrix_gpu = gpuinv3x3(arrayFullCross_vec.flatten('F'),N**2)
## First reshape
invCrossMatrix_temp = invCrossMatrix_gpu.reshape(N**2,3,3)
# Second reshape : don't forget ".T" transpose operator
invCrossMatrix = (invCrossMatrix_temp.reshape(N,N,3,3)).T
Question 1) Why the -F option into flatten('F') is necessary?
If I do only gpuinv3x3(arrayFullCross_vec.flatten,N**2), the code doesn't work. Python is maybe column major like Fortran ?
Question 2) Now, I would like to convert the following block:
## First reshape
invCrossMatrix_temp = invCrossMatrix_gpu.reshape(N**2,3,3)
# Second reshape : don't forget ".T" transpose operator
invCrossMatrix = (invCrossMatrix_temp.reshape(N,N,3,3)).T
into a single reshape instruction. Is it possible?
The issue is about to convert the 1D array invCrossMatrix_gpu(N**2 * 3 *3) directly into a (3,3,N,N) array.
I expect to reshape the original 1D array in one only time since I call these routines a lot of times.
Update
Is to right to say that array inVCrossMatrix defined by:
invCrossMatrix = (invCrossMatrix_temp.reshape(N,N,3,3)).T
has dimensions (3,3,N,N).
#hpaulj: Is it equivalent to do this?
invCrossMatrix =(invCrossMatrix_temp.reshape(N,N,3,3)).transpose(2,3,0,1)