could you define covariance? I know I could look it up, but maybe if you explain what it is, it'll help with your understanding.
However, you can show that with a system of linear equations:
x (amount invested in A)
y (amount invested in B)
.12x + .10y = .11 (x+y)
.01x - .01y = 0
x - y = 0
x = y
so the man invested equal amounts in A and B.
Ask if you need more help, although I haven't yet taken a university stats.