Matrix: Check sum

Checks if the sum of values in a given row matches the sum of values in the corresponding column.

Exercise

• A method takes an input parameter that is a matrix of integers where the number of rows are equal to the number of columns. e.g. 3 rows and 3 columns, 7 rows and 7 columns. The method returns true if the sum of all elements in each row matches the sum of all elements in the corresponding column. Otherwise, it returns false.
• Share and explain the time and space complexities for your solution in the comments above the method.
  • If the complexity is defined in terms of n, be sure to explain what n stands for.
• If you think of multiple approaches to solve the problem, implement the solution which minimizes space complexity. Explain the other approaches, and your decision in comments above the code.
• For example,
  • In an input matrix with 2 rows and 2 columns, if the sum of all elements in the row at index 0 matches the sum of all elements in the column at index 0, and the sum of all elements in the row at index 1 matches the sum of all elements in the column at index 1, then the method will return true.
  • Consider the example input:

  1 2 3 4
  9 5 3 1
  0 3 5 6
  0 8 3 6
  

    * In the above example case, the method should return `true`. (Sum of 0th row and 0th column is 10, sum of 1st row as well as the 1st column is 18 and so on.)