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 nonzero number
Example  R _{ 1 } →2R _{ 1 } , C _{ 3 } →(8)/5 C _{ 3 }

Add a row or column to another, multiplied by a nonzero
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 nonzero number
Add a row or column to another, multiplied by a nonzero number
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