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*A signature matrix is a diagonal elements are <math>\pm</math>
*A signature matrix is a diagonal elements are <math>\pm</math>
*So signature matrix is of the form:
*So signature matrix is of the form:
<math>\begin{pmatrix}
\pm & 0 & \cdots & 0 & 0 \\
0 & \pm & \cdots & 0 & 0 \\
\vdots & \ddots & \vdots \\
0 & 0 & \cdots & \pm & 0 \\
0 & 0 & \cdots & 0 & \pm
\end{pmatrix}</math>
*Any such matrix is its own inverse, hence is an involutory matrix.
*Any such matrix is its own inverse, hence is an involutory matrix.
*It is consequently a square root of the identity matrix.
*It is consequently a square root of the identity matrix.