Consider the matrix A = [(3,1)(-1,2)] (i) Find A^2 (ii) Find k so that A^2 = kA - 7I

Question

Consider the matrix A = \(\begin{bmatrix} 3 & 1 \\ -1 & 2 \\ \end{bmatrix} \)

(i) Find A²

(ii) Find k so that A² = kA – 7I

Answer 1

(ii) A² = KA -7I

⇒ 3k - 7 = 8 ⇒ 3k = 15 ⇒ k = 5