Compute the following matrix?

Did you leave out spaces on the second matrix?  The left side looks like you're multiplying a 3x2 matrix by a 2x2 matrix, which will give you another 3x2 matrix; but the matrix after the + appears to be a 3x1 matrix.  You can't add a 3x2 matrix to a 3x1 matrix.  If you meant:

    [ 3 -3 ]  [-1 -2 ]       [ 1  2 ]

    [ 1  2 ]  [  3 -1 ]  +  [ 3  4 ]

    [ 1 -3 ]                   [ 5  6 ]

...then the addition is legal.  The product on the left is:

    [ ((3)(-1) + (-3)(3))   ((3)(-2) + (-3)(-1)) ]

    [ ((1)(-1) + (2)(3))    ((1)(-2) + (2)(-1))  ]

    [ ((1)(-1) + (-3)(3))   ((1)(-2) + (-3)(-1)) ]

       [ (-3 - 9)  (-6 + 3) ]      [ -12  -3 ]

    = [ (-1 + 6)  (-2 - 2) ]  =  [    5  -4 ]

       [ (-1 - 9)  (-2 + 3) ]      [ -10   1 ]

Add the second 3x2 matrix to get:

        [-11  -1 ]

    =  [  8    0 ]

        [ -5    7 ]

I can't guess this kind of matrix !