If `A = [(a,b),(c,d)]` then find the value of `|A|^(-1)`

Answer

To find the value of \( |A|^{-1} \) for the matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), we will follow these steps:

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

### Step 2: Find the Inverse of the Determinant
We need to find \( |A|^{-1} \), which is the reciprocal of the determinant calculated in Step 1. Thus, we have:
\[ |A|^{-1} = \frac{1}{|A|} = \frac{1}{ad - bc} \]

### Final Result
Therefore, the value of \( |A|^{-1} \) is:
\[ |A|^{-1} = \frac{1}{ad - bc} \]

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