MATLAB: What is the mistake,

Given two real square matrix of order n. Get a new matrix of the elements of each column of the first matrix times elements of the corresponding rows of the second matrix. i coded using matlab but unfortunately it applys only for (3×3)matrix.what should i do so that it may apply for every kind of matrix, for example(4×4),(5×5) and more.
codes
 clc
clear
a=[1 2 3;4 5 6;7 8 9];
b=[1 2 3;4 5 6;7 8 9];
for i=1:length(a)
    for j=1:length(b)
      c(i,j)=a(i,j)*b(j,i)
  end
end
disp(a);
disp(b); 
disp(c);

Best Answer

I'll suggest your mistake is one of definition.
What do you expect when you multiply the elements of the first column with the elements of the first row? In your example, there are 3 products, so that multiplication must result in a vector of length 3.
Oh, do you want to add the elements too? In that case, this is just a matrix multiply.
Taking the columns of matrix a times the rows of matrix b, we get simply:
c = b*a;
Learn to use MATLAB!
Do you wish to compute it using loops for homework? While I don't do your homework, you have made a credible effort.
a=[1 2 3;4 5 6;7 8 9];
b=[1 2 3;4 5 6;7 8 9];
sa = size(a,2);
sb = size(b,1);
c= zeros(sa,sb);
for i=1:sa
  for j=1:sb
    c(i,j)=dot(a(:,i),b(j,:));
  end
end
Note my use of size instead of length. length is dangerous here. (Read the help for length to understand why.) As well, I used a dot product. Finally, see that I preallocated c with zeros. This is important.
Your teacher won't even let you use dot?
a=[1 2 3;4 5 6;7 8 9];
b=[1 2 3;4 5 6;7 8 9];
sa = size(a,2);
sb = size(b,1);
sk = size(a,1);
c= zeros(sa,sb);
for i=1:sa
  for j=1:sb
    for k = 1:sk
      c(i,j)= c(i,j) + a(k,i)*b(j,k);
    end
  end
end
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