D. Matrix diagonalization is useful in many computations involving matrices, because multiplying diagonal matrices is quite simple compared to multiplying arbitrary square matrices.

How is diagonalization useful?

A "simple" form such as diagonal allows you to instantly determine rank, eigenvalues, invertibility, is it a projection, etc. That is, all properties which are invariant under the similarity transform, are much easier to assess.

What does a diagonal matrix tell us?

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. ... Equivalently, we can define a diagonal matrix as a matrix that is both upper- and lower-triangular. The identity matrix In and any square zero matrix are diagonal. A one-dimensional matrix is always diagonal.