Consider the Following Symmetric and Idempotent Matrix A: a = $\frac { 1 } { n }$

Essay

Consider the following symmetric and idempotent Matrix A: A = I - $\frac { 1 } { n }$ ??' and ? = $\left[ \begin{array} { c } 1 \\1 \\\ldots \\1\end{array} \right]$ a. Show that by postmultiplying this matrix by the vector Y (the LHS variable of the OLS regression), you convert all observations of Y in deviations from the mean.
b. Derive the expression Y'AY. What is the order of this expression? Under what other name have you encountered this expression before?