Find the number of ordered quadruples $(a,b,c,d)$ of real numbers such that
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}^2 = \begin{pmatrix} c & a \\ d & b \end{pmatrix}.\]
Question:
Find the number of ordered quadruples $(a,b,c,d)$ of real numbers such that
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}^2 = \begin{pmatrix} c & a \\ d & b \end{pmatrix}.\]
Answer:
Let's think step by step.

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4
Find the number of ordered quadruples $(a,b,c,d)$ of real numbers such that
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}^2 = \begin{pmatrix} c & a \\ d & b \end{pmatrix}.\]
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