Question

Find an example of a 2 2 matrix with real number entries that is not diagonalizable over the real numbers.

Answer 1

Answer:

matrix multiplication is not commute​.

Step-by-step explanation:

without ambiguity. Due to associativity, matrices form a semigroup under multiplication. Since matrices form an Abelian group under addition, matrices form a ring. However, matrix multiplication is not, in general, commutative (although it is commutative if and are diagonal and of the same dimension.)