J, 19 bytes

(]/:~"1/:)"_ 1],:/:

Try it online!

J, 19 bytes

(]/:~"1/:)"_ 1],:/:

Try it online!

• Main verb ]/:~"1/:
  • The right most /: sorts the left arg (matrix) according to the order that would sort the right arg (specified order). This sorts rows.
  • Now that result get sorted /:~"1 again according to the order specified ]. But this time we're sorting with rank 1, ie, we're sorting each row, which has the effect of sorting columns.
• ],:/: We apply the above using both the order specified ] and the grade up of the order specified /:. This gives us the 2 results we want.