A is a square matrix satisfying the equation A2 - 4A - 5I = 0. then A-1 =

A2−4A−5I=0⇒A(A−4I)=5I⇒A−1=15(A−4I)

A is a square matrix satisfying the equation A2 - 4A - 5I = 0. then A-1 =

A2−4A−5I=0⇒A(A−4I)=5I⇒A−1=15(A−4I)

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A is a square matrix satisfying the equation A² - 4A - 5I = 0. then A^-1 =

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1/4(A-4I)

A-4I

1/3(A-4I)

1/5(A-4I)

answer is D.

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$A^{2} - 4 A - 5 I = 0 \Rightarrow A (A - 4 I) = 5 I \Rightarrow A^{- 1} = \frac{1}{5} (A - 4 I)$

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A is a square matrix satisfying the equation A2 - 4A - 5I = 0. then A-1 =

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A is a square matrix satisfying the equation A² - 4A - 5I = 0. then A^-1 =