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ISI2016-DCG-33

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Suppose $A$ and $B$ are orthogonal $n\times n$ matrices. Which of the following is also an orthogonal matrix? Assume that $O$ is the null matrix of order $n\times n$ and $I$ is the identity matrix of order $n.$

  1. $AB-BA$
  2. $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$
  3. $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$
  4. $A^{2}-B^{2}$
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