# Cross Product of Generator Matrix

Hello, I want to do the following items:

1. Take the matrices of SL(2,5)
2. Multiply them with identity
3. Add a specific matrix to the list
4. Check if the group of generatos and the specific matrix produce a finite group or not

Here is my code:

from sage.all import *
from sage.groups.matrix_gps.matrix_group import is_MatrixGroup
from sage.matrix.action import MatrixMatrixAction

cnot_np = matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]) #my specific matrix
print(cnot_np)
new_matrices_ = []
print(MatrixGroup(SL(2,5)))
gens_ = MatrixGroup(SL(2,5)).gens() #I got the matrix of my group (my group is binary icosahedral)
print(len(gens_))
identity_mat = matrix([[1, 0], [0, 1]]) #identity matrix
print(identity_mat.cross_product(identity_mat))
for i in gens_:
print(i)
tensor_mat_ = i.cross_product(identity_mat) #tensor product of matrices of binary icosahedral with identity
new_matrices_.append(tensor_mat_) #add them into a new list
new_matrices_.append(cnot_np)   # add the specific matrix to the list
is_infinite(new_matrices) #check if it generates an infinite group


However, I can't multiply the generator matrix with identity Here is my error message: AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'cross_product' How to solve this problem? Thanks in advance

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