Introduction In a recent article MacKinnon [I] describes four methods that may be
used to find square roots of 2 x 2 matrices. The first of these methods requires that
the matrix for which the square roots are sought be diagonalizable and, subsequently,
this method was used by Scott 121 to determine all the square roots of 2 X 2 matrices.
A surprising conclusion is that scalar 2 x 2 matrices possess double-infinities of
square roots whereas nonscalar 2 x 2 matrices have only a finite number of square
roots.