# Show that the matrix A = [(2, 3), (1, 2)] satisfies the equation A^2 – 4A + I = O,

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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.

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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