This paper considers a vector Gaussian channel of fixed identity covariance matrix and binary input signalling as the mean of it. A linear transformation is performed on the vector input signal. The objective is to find the optimal scaling matrix, under the total time constraint, that would: i) maximize the mutual information between the input and output random vectors, ii) maximize the MAP detection. It was found that the two metrics lead to different optimal solutions for our experimental design problem. We have used the Monte Carlo method for our computational work.