Ononot — By the Cayley–Hamilton theorem, a matrix satisfies its own c

Guest Session: 1 Question Remaining. Create Account to save progress.

Matricesmedium

0:00.0

By the Cayley–Hamilton theorem, a matrix satisfies its own characteristic polynomial. For a $2 \times 2$ matrix $A$ with characteristic polynomial $\det(A - \lambda I) = \lambda^2 - 5\lambda + 6$ , the relation $A^2 - 5A + 6I = 0$ holds, so $A^2 = 5A - 6I$ . Express $A^3$ in the form $cA + dI$ .