L14Q2_RecognizeIdentityMatrix.py

# By Ashwath from forums
# Given a list of lists representing a n * n matrix as input,
# define a  procedure that returns True if the input is an identity matrix
# and False otherwise.

# An IDENTITY matrix is a square matrix in which all the elements
# on the principal/main diagonal are 1 and all the elements outside
# the principal diagonal are 0.
# (A square matrix is a matrix in which the number of rows
# is equal to the number of columns)

def is_identity_matrix(matrix):
    #n x n check
    if len(matrix) != len(matrix[0]):
        return False
    else:
        #counts numbers of 1, must be equal to length of matrix
        counter = 0
        for i in matrix:
            counter += i.count(1)

        if counter != len(matrix):
            return False

        #now checks for positions in diagonal
        else:
            i = 0
            #print len(matrix)
            #print i
            while i < len(matrix):
                if matrix[0][0] == matrix[i][i]:
                    i += 1
                    #print i
                else:
                    return False

            return True



# Test Cases:

matrix = [[1,0,0,0],
           [0,1,0,0],
           [0,1,0,0],
           [0,0,0,1]]
print is_identity_matrix(matrix)
#>>>False

matrix1 = [[1,0,0,0],
           [0,1,0,0],
           [0,0,1,0],
           [0,0,0,1]]
print is_identity_matrix(matrix1)
#>>>True

matrix2 = [[1,0,0],
           [0,1,0],
           [0,0,0]]

print is_identity_matrix(matrix2)
#>>>False

matrix3 = [[2,0,0],
           [0,2,0],
           [0,0,2]]

print is_identity_matrix(matrix3)
#>>>False

matrix4 = [[1,0,0,0],
           [0,1,1,0],
           [0,0,0,1]]

print is_identity_matrix(matrix4)
#>>>False

matrix5 = [[1,0,0,0,0,0,0,0,0]]

print is_identity_matrix(matrix5)
#>>>False

matrix6 = [[1,0,0,0],
           [0,1,0,1],
           [0,0,1,0],
           [0,0,0,1]]

print is_identity_matrix(matrix6)
#>>>False

matrix7 = [[1, -1, 1],
           [0, 1, 0],
           [0, 0, 1]]
print is_identity_matrix(matrix7)
#>>>False