Question 635548
First of all, this problem has <i>nothing</i> to do with Trigonometry. Please try to post your problems in a relevant category. You will get faster, better responses when problems are posted in the right categories.<br>
{{{A= (matrix(3, 3, 3, -2, 4,
                 6,  1,  0,
                 -5,  9,  5))}}}
{{{B = (matrix(3, 3, 1,  5,  0,
                      -8,  4,  7,
                      2,  3,  -9))}}}
{{{C = (matrix(3, 3, 3, -2,  -7,
                     -4,  5,  1,
                     3,  0,  6))}}}<br>
{{{2B = 2*(matrix(3, 3, 1,  5,  0,
                        -8,  4,  7,
                        2,  3,  -9)) =
          (matrix(3, 3, 2,  10,  0,
                        -16,  8,  14,
                         4,  6,  -18))}}}<br>
{{{3C = 3*(matrix(3, 3, 3,  -2,  -7,
                        -4,  5,  1,
                        3,  0,  6)) =
          (matrix(3, 3, 9, -6,  -21,
                       -12,  15,  3,
                        9,  0,  18))}}}<br>
{{{2B+3C = (matrix(3, 3, 2,  10,  0,
                        -16,  8,  14,
                         4,  6,  -18)) +
           (matrix(3, 3, 9, -6,  -21,
                         -12,  15,  3,
                         9,  0,  18)) =
           (matrix(3, 3, 11, 4, -21,
                         -28, 23, 17,
                         13, 6, 0))}}}<br>
{{{D = A(2B+3C) = (matrix(3, 3, 3, -2, 4,
                 6,  1,  0,
                 -5,  9,  5)) *
              (matrix(3, 3, 11, 4, -21,
                           -28, 23, 17,
                           13, 6, 0))}}}
If all you care about is {{{d[23]}}} then all you need to is multiply the 2nd row of the first matrix times the 3rd row of the second matrix:
{{{d[23] = 6*(-21)+1*17+0*0 = -126 + 17 + 0 = -109}}}<br>
Here's the full multiplication of the two matrices:
{{{D = A(2B+3C) = (matrix(3, 3, 3, -2, 4,
                 6,  1,  0,
                 -5,  9,  5)) *
              (matrix(3, 3, 11, 4, -21,
                           -28, 23, 17,
                           13, 6, 0)) =
              (matrix(3, 3, 3*11 + -2*(-28)+4*13, 3*4 + -2*23+4*6, 3*(-21) + -2*(-21)+4*0, 
                            6*11+1*(-28)+0*13, 6*4+1*23+0*6, 6*(-21)+1*17+0*0, 
                            -5*11+9*(-28)+5*13, -5*4+9*23+5*6, -5*(-21)+9*17+5*0)) =
             (matrix(3, 3, 141, -10, -21,
                           38, 47, -109,
                           -242, 217, 258))}}}