Linear Algebra

A $2 \times 2$ matrix $A$ has the characteristic equation $\lambda^2 - 5\lambda + 6 = 0$. By the Cayley–Hamilton theorem, the inverse matrix $A^{-1}$ can be expressed as:

Options:

• (A) $\frac{1}{6}(5I - A)$
• (B) $\frac{1}{6}(A - 5I)$
• (C) $5A - 6I$
• (D) $\frac{1}{5}(6I - A)$