Output FormatReturn the absolute difference between the sums of the matrix's two diagonals as a single integer.

To solve the problem of finding the absolute difference between the sums of the two diagonals of a square matrix, we can follow these steps:

1. Break Down the Problem

1.1. Identify the two main diagonals in the matrix:

• Primary Diagonal: The diagonal that runs from the top left to the bottom right of the matrix.
• Secondary Diagonal: The diagonal that runs from the top right to the bottom left of the matrix.

1.2. Calculate the sum of the elements in each diagonal.

1.3. Compute the absolute difference between the two sums.

2. Relevant Concepts

• For a square matrix $A$ of size $n \times n$:
  • The elements in the primary diagonal are $A[i][i]$.
  • The elements in the secondary diagonal are $A[i][n-i-1]$.

3. Analysis and Detail

3.1. Let’s denote the primary diagonal sum as: $\text{Primary Diagonal Sum} = \sum_{i=0}^{n-1} A[i][i]$

3.2. For the secondary diagonal sum, we have: $\text{Secondary Diagonal Sum} = \sum_{i=0}^{n-1} A[i][n-i-1]$

3.3. The absolute difference $D$ can be calculated as: $D = \left| \text{Primary Diagonal Sum} - \text{Secondary Diagonal Sum} \right|$

4. Verify and Summarize

4.1. After calculating the two sums, ensure that the values are computed correctly.

4.2. Summarize the final result into a single integer which represents the absolute difference between the two sums.

Final Answer

Given a square matrix, you will compute and display the absolute difference, $D$, as follows: $D = \left| \sum_{i=0}^{n-1} A[i][i] - \sum_{i=0}^{n-1} A[i][n-i-1] \right|$ where $n$ is the dimension of the square matrix $A$.