Let the matrix \( A = \begin{bmatrix} 1 & 4 \\ 2 & -1 \end{bmatrix} \).
Statement-I: \( A^2 = 9I \)
Statement-II: The eigen values of \( A \) are \( -3 \) and \( 3 \)
The correct answer is
Show Hint
By the Cayley-Hamilton Theorem, if a matrix satisfies \( A^2 = 9I \), its matrix characteristic equation is \( \lambda^2 - 9 = 0 \). Solving this directly yields eigenvalues \( \lambda = \pm 3 \) instantly without needing separate determinant expansion calculations!