COMMENT this illustrates some SPSS matrix manipulations.
MATRIX.
 COMPUTE A={1, 1, 1; 
            2, 4, 8; 
            3, 9, 27}.
 PRINT A.
 COMPUTE B={1, 2, 3;
            2, 3, 4;
            3, 4, 5}.
   PRINT B.
 COMPUTE RANKA=RANK(A).
   PRINT RANKA.
 COMPUTE RANKB=RANK(B).
   PRINT RANKB.
 COMPUTE INVA=INV(A). 
   PRINT INVA.
 COMPUTE D=INVA*B.
   PRINT D.
 COMPUTE RANKD=RANK(D).
   PRINT RANKD.
 COMPUTE E=A*D.
   PRINT E.
END MATRIX.