M ab

    | 5  7|      |-2  1  0|
A = |-3  2|  B = | 5  9 -6|

M example

| 5  7|   |-2  1  0|   |     |
|-3  2| * | 5  9 -6| = |     |

M example 2 work

    |4  .5 -2|      |-3|
D = |12  1  3|  E = |34|
    |.5  2 -2|      | 1|

Do: 

     D * E = F

     D is 3x3
     E is 3x1

     3x3 .. 3x1
       -    -

It works. F will be a matrix 3x1

     |4  .5 -2|   |-3|   |  |
     |12  1  3| * |34| = |  |
     |.5  2 -2|   | 1|   |  |

     4(-3) + .5(34) + -2(1) =
     -12   + 17     + -2    = 3

     12(-3) + 1(34) + 3(1)  =
     -36    + 34    + 3     = 1

     .5(-3) + 2(34) + -2(1) =
     -1.5   + 68    + -2    = 64.5

     |4  .5 -2|   |-3|   |  3 |
     |12  1  3| * |34| = |  1 |
     |.5  2 -2|   | 1|   |64.5|

         |  3 |
     F = |  1 |
         |64.5|

M example work

      | 5  7|   |-2      |   |*    |
      |     | * | 5      | = |     |

Such that:

     5(-2) + 7(5) = 
     -10   + 35   = 25

So:

     | 5  7|   |-2  1  0|   |25    |
     |-3  2| * | 5  9 -6| = |      |

The top middle element of the result will be equal to the top row of A 
times the middle column of B... 

     5(1) + 7(9) = 
     5    + 63   = 68

So:

     | 5  7|   |-2  1  0|   |25 68   |
     |-3  2| * | 5  9 -6| = |        |

And finally for the top row, the top right element will be equal to the 
top row of A times the right column of B...

     5(0) + 7(-6) = 
     0    + -42   = -42

So:

     | 5  7|   |-2  1  0|   |25 68 -42|
     |-3  2| * | 5  9 -6| = |         |

Now we do exactly the same for the bottom row. The bottom row of A will 
be multiplied by each column of B

So:

     -3(-2) + 2(5) =
     6      + 10   = 16

     -3(1) + 2(9)  =
     -3    + 18    = 15

     -3(0) + 2(-6) =
     0     + -12   = -12

     | 5  7|   |-2  1  0|   |25 68 -42|
     |-3  2| * | 5  9 -6| = |16 15 -12|

So Matrix C equals:

         |25 68 -42|          
     C = |16 15 -12|