def inverse(A):
if not A or len(A) != len(A[0]):
raise Exception("Invalid input")
length = len(A)
res = append(A, eye(length))
for i in range(length):
res[i] = Vector.multiply_integer(res[i], 1 / res[i][i])
for j in range(length):
if i == j:
continue
res[j] = Vector.minus(res[j], Vector.multiply_integer(res[i], res[j][i]))
for i in range(length):
res[i] = res[i][length:]
return res
def determinant(A):
if not A or len(A) != len(A[0]):
raise Exception("Invalid input")
new_A = [[0] * len(A[0]) for _ in range(len(A))]
for i in range(len(A)):
for j in range(len(A)):
new_A[i][j] = A[i][j]
for i in range(len(A)):
for j in range(i + 1, len(A)):
new_A[j] = Vector.minus(new_A[j], Vector.multiply_integer(new_A[i], new_A[j][i] / new_A[i][i]))
res = 1
for i in range(len(A)):
res *= new_A[i][i]
return res
