A' is a diagonal matrix, and Q^-1 is a matrix on the left to change rows, and P is a matrix on the right to change columns. Therefore, the question is asking that getting a diagonal matrix (only have diagonal entries, and rest entries are 0) from any matrix A, only with it self transformation among its columns and rows, to shows that d1 is the gcd of all entries of A.

If died,....d are the diagonal entries in the matrix A = Q AP, show that d is the greatest common divisor of all the entries a; of A