The following problems use IML matrix notation. That is, we use {} for
the parentheses that usually border the elements of a matrix. Also, rows
are delimited by the "," symbol. That is, A={2 4, 3 1} represents the
matrix:
                   /        \
                   | 2    4 |
                   | 3    1 |
                   \        / 

1. Find the determinant of the matrix A in each case:

   a) Let A={2 4, 3 1}. 
   b) Let A={1 3, 6 4}.
   c) Let A={3 1 6, 7 4 5, 2 -7 1}.
   d) Let A={3 2 1, 2 1 -3, 4 0 1}.

   Solution:

   a) |A| = 2(1) - 4(3) = -10
   b) |A| = 1(4) - 3(6) = -14
   c) |A| = 3*|4 5, -7 1|(-1)^2 + 1*|7 5, 2 1|(-1)^3 
                    + 6*|7 4, 2 -7|(-1)^4
          = 3(39) - 1(-3) + 6(-57)
          = -222
   d) |A| = 3*|1 -3, 0 1|(-1)^2 + 2*|2 -3, 4 1|(-1)^3
                    + 1*|2 1, 4 0|(-1)^4
          = 3(1) - 2(14) + 1(-4)
          = -29


2. Find the inverse of the matrix A={2 3, 1 5}.

   Solution:

   Since |A| = 2(5) - 1(3) = 7 then:

   A(-1) = {5/7 -3/7, -1/7 2/7}