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

Explanation

To find the inverse of the given matrix, we will follow these steps:

1. **Define the Matrix**:
Let \( A = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix} \).

2. **Calculate the Determinant of A**:
The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is calculated using the formula:
\[ \text{det}(A) = ad - bc \]
For our matrix:
\[ \text{det}(A) = (2)(2) - (4)(1) = 4 - 4 = 0 \]

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

4. **Determine the Inverse**:
The inverse of a matrix \( A \) is defined as:
\[ A^{-1} = \frac{\text{adj}(A)}{\text{det}(A)} \]
However, since the determinant is 0, we cannot compute the inverse. Therefore, the inverse of matrix \( A \) is **not defined**.

### Final Answer:
The inverse of the matrix \( A = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix} \) is **not defined**.

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