Matrix multiplication

Run and explain the following:

A = randn(1000);

tic
  for k = 1:10
    C = A' * A;
  end
toc

tic
  for k = 1:10
    C = A * A';
  end
toc

tic
  for k = 1:10
    C = A * A;
  end
toc

and the following

A = rand(1000);
B = rand(1000);

tic
  for k = 1:10
    C = A * B;
  end
toc

A = single(A);
B = single(B);

tic
  for k = 1:10
    C = A * B;
  end
toc



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