Let A be an orthogonal square matrix.

Statement-1: $A^{-1}$ is an orthogonal matrix.

Statement-2: $(A^{-1})=(A^T)^{-1}$ and $(AB)^{-1}=B^{-1} A^{-1}$

Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Clearly, statement-2 is true. Since A is an orthogonal matrix.

$∴AA^T = A^TA =I$

$⇒(AA^T)^{-1}=(A^TA)^{-1} = I$

$⇒(A^T) A^{-1}=A^{-1} (A^T)^{-1}$   $[∵ (AB)^{-1} = B^{-1} A^{-1}]$

$⇒(A^{-1})^T A^{-1}=A^{-1} (A^{-1})^T$   $[∵ (A^T)^{-1}=(A^{-1})^T]$

$⇒A^{-1}$ is orthogonal.