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Like many other programming languages, the indices in Python arrays starts at 0. This is commonly known, but may catch you by surprise if you're used to the indices in e.g. Matlab.

mat1 = [[1, 2, 3], [4, 5, 6]]
# To make the matrices easier to read while coding, we can place the different lists vertical to eachother instead of horizontally.
mat2 = [[1, 2, 3],
	   [4, 5, 6]]

# Printing both of these matrices will result in the same output:
[[1, 2, 3], [4, 5, 6]]

# To alter the output to a more readable format, for-loops are very helpful:
[[1, 2, 3], 
[4, 5, 6]]

A = [[1, 2, 3], 
	[4, 5, 6]]

print("A =", A) 				# Whole matrix
print("A[1] =", A[1])      		# 2nd row
print("A[1][2] =", A[1][2])   	# 3rd element of 2nd row
print("A[0][-1] =", A[0][-1])   # Last element of 1st Row

column = [];        			# Empty list
for row in A:
  column.append(row[2])   		# Adding the element in the third column of every row-list.

print("3rd column =", column)

A = [[1, 2, 3], [4, 5, 6]]
A[1] = [4, 5, 6]
A[1][2] = 6
A[0][-1] = 3
3rd column = [3, 6]

a = np.array([[1,2],[3,4]])

b = a[0,1]

np.linalg.solve(a,b) #where a and b is matrixs


#returns a array with solutions to the system

np.linalg.eig(a) # where a is a square matrix


#returns two arrays [v,w]
#v containing the eigenvalues of a
#w containing the eigenvectors of a

np.linalg.det(a) # where a is a square matrix


#returns the determinant of the matrix a

np.linalg.inv(a) # where a is the matrix to be inverted


#Returns the inverse matrix of a

import numpy as np

# Solving following system of linear equation
# 5a + 2b = 35
# 1a + 4b = 49

a = np.array([[5, 2],[1,4]]) # Lefthand-side of the equation
b = np.array([35, 94]) #Righthand-side

print(np.linalg.solve(a,b)) #Printing the solution