Elementary operations on a matrix

We use elementary operations to find inverse of a matrix

The elementary matrix operations are

• Interchange two rows, or columns
  Example - R ₁ ↔ R ₃ , C ₂ ↔ C ₁
  
  
• Multiply a row or column by a non-zero number
  Example - R ₁ →2R ₁ , C ₃ →(-8)/5 C ₃
  
  
• Add a row or column to another, multiplied by a non-zero
  Example - R ₁ → R ₁ − 2R ₂ ,  C ₃ → C ₃ + 2/3 C ₁
  
  

Let’s look at each one of them in detail

Interchange rows or column

Multiply a row or column by a non-zero number

Add a row or column to another, multiplied by a non-zero number