If for the Matrix A, A3 = I, Then A−1 = - Mathematics

Question

If for the matrix A, A³ = I, then A⁻¹ = _____________ .

Options

A²
A³
A
none of these

MCQ

Solution

A²

\[\text{ Given: }\hspace{0.167em} A^3 = I \]

\[ \Rightarrow A^3 A^{- 1} = I A^{- 1}.......... \left[\text{Multiplying both sides by }A^{- 1} \right]\]

\[ \Rightarrow A^2 = A^{- 1}\]

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Properties of Matrix Multiplication - Inverse of a Square Matrix by the Adjoint Method

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Q 13 Q 12 Q 14

Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [Page 37]

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RD Sharma Mathematics [English] Class 12

Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 13 | Page 37

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