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Find the Determinant of a 2x2 Matrix

Certification: Basic Level Accuracy: 66.67% Submissions: 3 Points: 5

Write a C# program to calculate the determinant of a 2×2 matrix. The determinant of a 2×2 matrix [[a, b], [c, d]] is calculated as (a*d - b*c). The determinant is useful in many applications including solving systems of linear equations, finding inverse matrices, and determining if a matrix is invertible.

Example 1
    
        
  • Input: matrix = [
    
  [4, 6],
    
  [3, 8]
]
    • 
        
  • Output: 14
    • 
        
  • Explanation:
            
      
                
    • Step 1: Verify the input matrix is a 2×2 matrix.
      • 
                
    • Step 2: Extract the four elements of the matrix: a (top-left) = 4, b (top-right) = 6, c (bottom-left) = 3, d (bottom-right) = 8.
      • 
                
    • Step 3: Apply the determinant formula: det(A) = a*d - b*c.
      • 
                
    • Step 4: For the matrix [[4, 6], [3, 8]], the determinant is calculated as: 4*8 - 6*3 = 32 - 18 = 14
      • 
            
    
        
    •
Example 2
    
        
  • Input: matrix = [
    
  [1, 2],
    
  [3, 4]
]
    • 
        
  • Output: -2
    • 
        
  • Explanation:
            
      
                
    • Step 1: Verify the input matrix is a 2×2 matrix.
      • 
                
    • Step 2: Extract the four elements of the matrix: a (top-left) = 1, b (top-right) = 2, c (bottom-left) = 3, d (bottom-right) = 4.
      • 
                
    • Step 3: Apply the determinant formula: det(A) = a*d - b*c.
      • 
                
    • Step 4: For the matrix [[1, 2], [3, 4]], the determinant is calculated as: 1*4 - 2*3 = 4 - 6 = -2
      • 
            
    
        
    •
Constraints
    
        
  • matrix.length == 2
    • 
        
  • matrix[i].length == 2
    • 
        
  • -1000 ≤ matrix[i][j] ≤ 1000
    • 
        
  • Time Complexity: O(1)
    • 
        
  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
        
  • Verify the input matrix is a 2×2 matrix.
    • 
        
  • Extract the four elements of the matrix (a, b, c, d).
    • 
        
  • Apply the determinant formula: det(A) = a*d - b*c.
    • 
        
  • Handle potential integer overflow by using appropriate data types.
    • 
        
  • Return the calculated determinant.
    •

Steps to solve by this approach:

 Step 1: Validate the input to ensure it's a 2×2 matrix.
 Step 2: Extract the four elements from the matrix: a (top-left), b (top-right), c (bottom-left), d (bottom-right).
 Step 3: Apply the determinant formula for a 2×2 matrix: det(A) = ad - bc.
 Step 4: Ensure calculations handle potential integer overflow if necessary.
 Step 5: Return the calculated determinant value.

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