Question

Show that the matrix  A = [(2, 3), (1, 2)]  satisfies the equation A² – 4A + I = O, where I is 2 × 2 identity matrix and O is 2 × 2 zero matrix. Using this equation, find A^–1.

Answer 1

Given that

Now, A² - 4A + I = 0

⇒ AA - 4A = -I

⇒ AA(A^-1) - 4AA^-1 = - IA^-1(Post multiplying by A^–1 because |A| ≠ 0)

⇒ A(AA^-1) - 4I = - A^-1

⇒ AI - 4I = - A^-1