Question

If \( A = \begin{bmatrix} 4 & \lambda & -3 0 & 2 & 5 1 & 1 & 3 \end{bmatrix} \), then \( A^{-1} \) exists if:

• A. \( \lambda = 2 \)
• B. \( \lambda = 0 \)
• C. \( \lambda \ne 2 \)
• D. \( \lambda \ne -2 \)

Hint:

A matrix is invertible iff its determinant is non-zeroAlways compute determinant carefully using expansion.

Answer 1

The Correct Option is D