Isn't matrix multiplication already a convolution? You are rotating the right hand side matrix anti clockwise 90 degrees and then convolving it upon the LHS matrix from top to bottom.
The point above regarding convolution had to do specifically with accelerating 3x3 and above convolutional operations, as the product and the accumulation can be done in a few clock cycles if setup with care and love.
there is no way in which the indexes into the input matrices in a matrix multiplication are formed from sums or differences of indices and dummy variables
however, convolution is a matrix multiplication, specifically multiplication by the circulant matrix of the convolution kernel