Answer
True
Work Step by Step
Assume $A$ and $B$ are n × n orthogonal matrices, then $A^{-1}=A^T\\
B^{-1}=B^T$
If $A^{-1}, B^{-1}$ exist, $\det (A) \ne 0\\
\det (B) \ne 0\\
\rightarrow \det (AB)=\det (A) \times \det (B) \ne 0$
Therefore, $(AB)^{-1}$ exist.
Obtain: $(AB)^{-1}=B^{-1}A^{-1}\\
=B^TA^T\\
=(AB)^T$
Hence, $AB$ is an orthogonal matrix.
The statement is true.
