Prove that \( \mathrm{P} \) \[ \left[\begin{array}{lll} \hat{i} & \hat{k} & \hat{j} \end{array}\...

Prove that
\( \mathrm{P} \)
\[
\left[\begin{array}{lll}
\hat{i} & \hat{k} & \hat{j}
\end{array}\right]=\left[\begin{array}{lll}
\hat{k} & \hat{j} & \hat{i}
\end{array}\right]=\left[\begin{array}{ll}
\hat{j} \hat{j} & \hat{k}
\end{array}\right]=1
\]