In reply to Mantana Seeno.

You'll have to be more specific. There are dozens of tests for multivariate normality. The crossproduct matrix alone is not sufficient for determining multivariate normality, since many distrivutions could have the same crossproduct matrix. However, the crossproduct matrix is used to form the covariance matrix, which is used to form Mahalanobis distances from observations to the multivariate mean. In MVN data, the distances fallow a chi-square distribution, and that can be used as a test of MVN normality.