Question

If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), then \( A^{-1} \) is:

• A. \( \begin{pmatrix} -2 & 1 \\ \frac{3}{2} & -\frac{1}{2} \end{pmatrix} \)
• B. \( \begin{pmatrix} 2 & 1 \\ \frac{3}{2} & -\frac{1}{2} \end{pmatrix} \)
• C. \( \begin{pmatrix} 2 & 1 \\ \frac{3}{2} & \frac{1}{2} \end{pmatrix} \)
• D. \( \begin{pmatrix} -2 & 1 \\ -\frac{3}{2} & -\frac{1}{2} \end{pmatrix} \)

Hint:

Remember the inverse formula for a 2x2 matrix. It's a fundamental operation. Pay close attention to signs when changing off-diagonal elements and when multiplying by the inverse of the determinant.

Answer 1

The Correct Option is A