As it happens with the univariate case, we should also check whether the covariance matrices are the same between the two samples. This obviously requires a more sophisticated test (compared to the univariate test), because we are now working with matrices. There are several possible strategies, although a simple one is to use Box's M test, which can be obtained via the heplots package.

We need to create a combined dataset and a grouping variable to use boxM:

library(heplots) 
class1$group = "1" 
class2$group = "2" 
combined = rbind(class1,class2) 
combined$group = as.factor(combined$group) 
boxM(cbind(combined$Math,combined$History,combined$Sociology)~group,data = combined) 

The preceding code generate the following output for testing the homogeneity of the covariance matrices. We don't reject the homogeneity assumption: 

Because the p-value is larger (much larger than 5%), we decide to accept the null hypothesis that the covariance matrices are the same between the two groups.