Consider the $4 \mathrm{x} 4$ square matrix below.

\[\left[\begin{array}{llll}A & B & C & D \\D & A & B & C \\C & D & A & B \\B & C & D & A\end{array}\right]\]

Suppose the rows correspond to subjects and that each subject is tested under experimental conditions represented by letters in the particular arrangement of the letters across rows. The columns correspond to time periods. It is known that the study outcome under the $\mathrm{B}$ condition preceded by the A condition is always lower.

a. Is the matrix a Latin Square design?

b. If treatments are randomly assigned to $\mathrm{A}$ through $\mathrm{D}$, will this result in an unbiased treatment effect? Explain.