import numpy as np

def det_rec(A):
    
    if A.shape==(2,2): return A[0,0]*A[1,1]-A[0,1]*A[1,0]
    
    det = 0.
    reduced = np.zeros((A.shape[0]-1,A.shape[1]-1))
    
    for i in range(A.shape[1]):
        reduced[:,:i] = A[1:,:i]
        reduced[:,i:] = A[1:,i+1:]
        r = A[0,i]*det_rec(reduced)
        
        if i % 2==1: det -= r
        else:        det += r
	
    return det
   
print('test #1 - simply check the output')
T = np.array([[1.,1.,2.],[2.,1.,1.],[1.,2.,1.]]) 
print('T =\n',T)
print('|T| =',det_rec(T))
print('-'*20)

print('test #2 - |A| = |A^T|')
A = np.random.rand(25).reshape((5,5))
print('|A| =',det_rec(A))
print('|A.T| =',det_rec(A.T))
print('-'*20)

print('test #3 - |A*B| = |A|*|B|')
B = np.random.rand(25).reshape((5,5))
print('|A*B| =',det_rec(A.dot(B)))
print('|A|*|B| =',det_rec(A)*det_rec(B))
print('-'*20)

print('test #4 - |A| does not change after row operation')
print('|A| =',det_rec(A))
A[1,:] += A[0,:]*0.5
print('|A| =',det_rec(A))
print('-'*20)