Using Math-based Approach :

By using math, we create two equations using the actual and expected sum and sum of squares. Solving these equations, we find the missing and repeating numbers.

1. Numbers in the matrix range from 1 to n². One number is repeating, and one number is missing.

2. Calculate:

expectedSum = n² * (n² + 1) / 2

expectedSquareSum = n² * (n² + 1) * (2n² + 1) / 6

3. Traverse the matrix to get

actualSum: Sum of all the numbers in a grid.

actualSquareSum: Sum of squares of all the numbers in a grid.

4. Let

diff = actualSum - expectedSum

diff = a - b

squareDiff = actualSquareSum - expectedSquareSum

squareDiff = a² - b²

5. Use:

squareDiff = a² - b² = (a+b)(a-b)

sum_ab = squareDiff / diff

= (a+b)(a-b)/(a-b)

= (a+b)

Solve:

a = (diff + sum_ab) / 2

b = (sum_ab - diff) / 2

6. At the end we return [a, b]

Repeat & Missing Number