find inverse using elementary operations` [[6,-3],[-2,1]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 6 & -3 \\ -2 & 1 \end{pmatrix} \) using elementary operations, we will follow these steps:

### Step 1: Calculate the Determinant of Matrix A
The determinant of a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is calculated using the formula:
\[ \text{det}(A) = ad - bc \]
For our matrix \( A \):
- \( a = 6 \)
- \( b = -3 \)
- \( c = -2 \)
- \( d = 1 \)

Calculating the determinant:
\[ \text{det}(A) = (6)(1) - (-3)(-2) = 6 - 6 = 0 \]

### Step 2: Check the Determinant
Since the determinant is \( 0 \), it indicates that the matrix \( A \) is singular, meaning it does not have an inverse.

### Conclusion
The inverse of the matrix \( A \) does not exist because the determinant is equal to zero.

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