Question

Linear Alg.
Give a 2x2 matrix A where this property holds true.
1) A^2 = A, all entries are nonzero
2) A ^3 = A, all entries are nonzero

For both, I can use the orthogonal projections, but when could I use the reflection matrix?

Answer 1

if \(A\) is a reflection, then \(A^2=AA=I\) so it would not satisfy 1. however, \(A^3=
AA^2=A\) would be satisfied

Answer 2

Again, you're the best.