On equivalence of pairs of matrices, which determinants are primes powers, over quadratic Euclidean rings.

We establish that a pair of matrices, which determinants are primes powers, can be reduced over quadratic Euclidean ring Κ = ℤ [√k] to their triangular forms with invariant factors on a main diagonal by using the common transformation of rows over a ring of rational integers ℤ and separate transformations of columns over a quadratic ring Κ. [ABSTRACT FROM AUTHOR]