Counting the 1s in each row of the incidence matrix of a 2-design

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Consider the $2 - (4t-1, 2t, t)$ design where $t$ is an odd number and $A$ is the incidence matrix. I suspect that the number of elements with value $1$ in each row of $A$ is equal to $2t$ but I can't prove it. Any comments and ideas will be greatly appreciated!