3. Determining Whether Matrices are Idempotent A square matrix is idempotent when
\(A ^ { 2 } = A\) . Determine whether each matrix is idempotent.
(a) \(\left[ \begin{array} { l r } { 1 } & { 0 } \\ { 0 } & { 0 } \end{array} \right]\)
(b) \(\left[ \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right]\) (c) \(\left[ \begin{array} { r r } { 2 } & { 3 } \\ { - 1 } & { - 2 } \end{array} \right]\) (d) \(\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 1 } & { 2 } \end{array} \right]\) (e) \(\left[ \begin{array} { l l l } { 0 } & { 0 } & { 1 } \\ { 0 } & { 1 } & { 0 } \\ { 1 } & { 0 } & { 0 } \end{array} \right]\)
