$\begin{array}{1 1}(A)\;A^t\text{ must be orthogonal}\\(B)\;A^t\text{ may not be orthogonal}\\(C)\;A^{-1}\text{ may not be orthogonal}\\(D)\;\text{None of the above}\end{array}$

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Since A is orthogonal matrix therefore $AA^t=A^tA=I$

$\Rightarrow (AA^t)^t=(A^tA)^t=I$

$\Rightarrow (AA^t)^t=(A^tA)^t=I$

$\Rightarrow (A^t)^tA=A^t.(A^t)^t=I$

$\Rightarrow A^t$ is orthogonal.

$((AA)^t)^{-1}=(A^tA)^{-1}=I$

$\Rightarrow (A^t)^{-1}.A^{-1}=A^{-1}.(A^t)^{-1}=I$

$\Rightarrow (A^{-t})^t.A^{-1}=A^{-1}.(A^{-1})^t=I$

Hence $A^{-1}$ is orthogonal.

Hence (D) is the correct answer.

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