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Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 30

Answers (1)

option (a) \begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix},if n is an even natural number.

Given -A=\begin{bmatrix} 2 &-1 \\ 3& -2 \end{bmatrix}

Hint – find the value of A2

Solution-A=\begin{bmatrix} 2 &-1 \\ 3& -2 \end{bmatrix}

\begin{aligned} &A^{2}=\left[\begin{array}{ll} 2 & -1 \\ 3 & -2 \end{array}\right]\left[\begin{array}{ll} 2 & -1 \\ 3 & -2 \end{array}\right] \\ &A^{2}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \\ &A^{2}=I \\ &\Rightarrow A^{-1}=A \end{aligned}

 

Therefore, when n is odd A^{n}=A^{-1}  and when n is even A^{n}=I

 

Hence, option (a) is correct

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