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Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise Fill in the blanks Question 2 Maths Textbook Solution.

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Answer  \rightarrow A^{2}

Hint  \rightarrow Determinant of non-singular matrix is non-zero

Given  \rightarrow A  is a non-singular matrix such that A^{3}=I

Explanation  \rightarrow A is a non-singular matrix, therefore  \left | A \right |\neq 0

                        \begin{aligned} &A^{3}=I \\ &A \cdot A^{2}=I \end{aligned}

                       A^{-1} A \cdot A^{2}=I \cdot A^{-1} \quad\left[A^{-1} A=A A^{-1}=I\right]
Hence,          \begin{aligned} A^{2} &=A^{-1} \\ A^{-1} &=A^{2} \end{aligned}


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