> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> A := matrix(3,3,[0, 2, -5, 0, -1,3, 1,0,0]);

                              [0     2    -5]
                              [             ]
                         A := [0    -1     3]
                              [             ]
                              [1     0     0]

> inverse(A);

                            [0    0    1]
                            [           ]
                            [3    5    0]
                            [           ]
                            [1    2    0]

> B := matrix(3,3);

                    B := array(1 .. 3, 1 .. 3, [])

> print(B);

                   [B[1, 1]    B[1, 2]    B[1, 3]]
                   [                             ]
                   [B[2, 1]    B[2, 2]    B[2, 3]]
                   [                             ]
                   [B[3, 1]    B[3, 2]    B[3, 3]]

> det(B);

  B[1, 1] B[2, 2] B[3, 3] - B[1, 1] B[2, 3] B[3, 2]

         - B[2, 1] B[1, 2] B[3, 3] + B[2, 1] B[1, 3] B[3, 2]

         + B[3, 1] B[1, 2] B[2, 3] - B[3, 1] B[1, 3] B[2, 2]

> C := matrix(3,3,[a,b,c, alpha, beta,gamma, X,Y,Z]);

                         [  a       b        c  ]
                         [                      ]
                    C := [alpha    beta    gamma]
                         [                      ]
                         [  X       Y        Z  ]

> det(C);

 a beta Z - a gamma Y - alpha b Z + alpha c Y + X b gamma - X c beta

> inverse(C);

  [-beta Z + gamma Y     b Z - c Y       b gamma - c beta]
  [----------------- ,   --------- ,   - ----------------]
  [       %1                %1                  %1       ]
  [                                                      ]
  [  -alpha Z + gamma X     a Z - c X   a gamma - c alpha]
  [- ------------------ , - --------- , -----------------]
  [          %1                %1              %1        ]
  [                                                      ]
  [-alpha Y + beta X     a Y - b X       a beta - b alpha]
  [----------------- ,   --------- ,   - ----------------]
  [       %1                %1                  %1       ]

  %1 := -a beta Z + a gamma Y + alpha b Z - alpha c Y - X b gamma

         + X c beta

>