In recent years, several articles are written about the root
of a matrix, and we can refer to [1-6] for instance. In 2007,
Kh. Ikramov tried to solve the matrix equation XX = I
and XX = I. At first, he considered the problem as
XX =
a b
c d
and then generalized it to general case
XX = In and XX = In [7]. If matrix A has different eigenvalues
λ1, λ2, ... , λn, then the root of A, i.e. solution of the
equation X2 = A is achieved as the following: