The unbiasedness and the monotonicity property of the power functions of a class of tests for the equality of covariance matrices of two $p$-variate normal distributions have been studied. For testing $\Sigma = I_p$ in a $p$-variate normal distribution with mean vector $\mu$ and covariance matrix $\Sigma$, a class of tests is proposed and their power functions and admissibility are studied.
"Properties of Tests Concerning Covariance Matrices of Normal Distributions." Ann. Statist. 1 (6) 1222 - 1224, November, 1973. https://doi.org/10.1214/aos/1176342572