\b[No.] In <characteristic three>, $X^3-1=(X-1)^3$. This is still the <minimal polynomial>, because the three cyclic <basis vectors> remain independent. Its repeated factor violates the <minimal polynomial criterion for diagonalizability>. Equivalently, the only possible <eigenvalue> is one; a diagonalizable matrix with that sole <eigenvalue> would be the <identity matrix>, whereas this matrix is not the identity.

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2006 / 1 / c / Solution

 Solution (source code)