`[{:(2,1),(4,2):}]` find the inverse of matrix

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix} \), we will follow these steps:

### Step 1: Calculate the Determinant of the Matrix
The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by the formula:
\[ \text{det}(A) = ad - bc \]
For our matrix \( A = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix} \):
- \( a = 2 \)
- \( b = 1 \)
- \( c = 4 \)
- \( d = 2 \)

Now, substituting these values into the determinant formula:
\[ \text{det}(A) = (2)(2) - (1)(4) = 4 - 4 = 0 \]

### Step 2: Check the Determinant
Since the determinant of matrix \( A \) is 0, we conclude that the matrix is singular.

### Step 3: Conclusion
If the determinant of a matrix is 0, the inverse of that matrix does not exist.

Thus, the inverse of the matrix \( A \) does not exist.

---