Merge matrices by matching first column values in MATLAB?

I have two matrices A and B, where they share some common values in the first column. I would like to merge these into one matrix giving only the values they have in common in the first column along with their respective values in the other columns. For example

A= 4  5.3
   5  7.3
   8  2.5
   9  4.7

B= 1  3.6  0.4
   2  3.9  0.6
   3  9.2  0.9
   4  5.1  0.1
   5  0.7  0.5
   6  8.3  0.7
   7  7.3  0.2
   8  1.6  0.6
   9  4.6  0.2

The output would be

C= 4  5.3  5.1  0.1
   5  7.3  0.7  0.5
   8  2.5  1.6  0.6
   9  4.7  4.6  0.2

My actual data sets are much longer but this is the general idea.

Thanks

Answer 1

[Robert]

A= [4  5.3
   5  7.3
   8  2.5
   9  4.7];

B= [1  3.6  0.4
   2  3.9  0.6
   3  9.2  0.9
   4  5.1  0.1
   5  0.7  0.5
   6  8.3  0.7
   7  7.3  0.2
   8  1.6  0.6
   9  4.6  0.2];

[~,ia,ib] = intersect(A(:,1),B(:,1));

C = [A(ia,1:2),B(ib,2:3)]

[Robert]

The difference between this answer and Azzi's is that this works even if not all values of the first column in A appear in the first column of B. Delete the last row of B to see the difference.

Answer 2

[Azzi Abdelmalek]

A= [4  5.3
 5  7.3
 8  2.5
 9  4.7]
B= [1  3.6  0.4
 2  3.9  0.6
 3  9.2  0.9
 4  5.1  0.1
 5  0.7  0.5
 6  8.3  0.7
 7  7.3  0.2
 8  1.6  0.6
 9  4.6  0.2]
B1=B(ismember(B(:,1),A(:,1)),:)
C=[A B1(:,2:3)]