HW3.sagews

m1 = matrix([ [20, 2], [5, 4] ])
m1.determinant()

m = matrix([ [1, 7, 22], [4, 9, 2], [1, 2, 5] ])
m.determinant()

70 -107

matrix(IntegerModRing(26),[ [2, 3], [1, 22] ]).inverse()

[24 5] [19 14]

matrix(IntegerModRing(26), [ [6, 24, 1], [13, 16, 10], [20, 17, 15] ]).inverse()

[ 8 5 10] [21 8 21] [21 12 8]

A = matrix([[21, 8], [19, 14]])
A1 = matrix([[10,23], [16, 24]])

A * A1

[338 675] [414 773]

key = matrix([[9,4], [5,7] ])

# A = matrix([[13], [5]])
# key * A % 26

frst = Matrix([[12],[4]])
sec = matrix([[4], [19]] )
third = matrix([[12], [4]])
fourth = matrix([[0], [19]])
fifth = matrix([[19], [7]])
sixth = matrix([[4], [20]])
seventh = matrix([[18],[20]])
eighth = matrix([[0],[11]])
ninth = matrix([[15],[11]])
tenth = matrix([[0],[2]])
ele = matrix([[4],[0]])
twe = matrix([[19],[19]])
thirt = matrix([[4],[13]])
fourt = matrix([[17],[0]])
fift = matrix([[19],[7]])
sixt = matrix([[4],[17]])
sevent = matrix([[19],[7]])
eight = matrix([[0],[13]])
nine = matrix([[4],[8]])
twent = matrix([[6],[7]])
twentone = matrix([[19],[14]])
twenttwo = matrix([[2] ,[11]])
twentthree = matrix([[14],[2]])
twentfour = matrix([[10],[23]])

c = key * frst % 26

[20] [10]

c = key * frst % 26
key.determinant()
k_inverse = matrix(IntegerModRing(26), [[9,4], [5,7] ]).inverse()
k_inverse * c % 26

43 [12] [ 4]