Find the intersect of two columns from different matrix but keep the corresponding cells from the same row along with the intercept values

I have two matrix with two columns. For example

A = [2 2; 4 3; 6 5; 8 3; 10 2]
B = [2 1; 3 2; 5 2; 8 2; 10 1]

I want to find the values from the first column that intersect. I can do this using 'C = intersect(A(:,1),B(:,1)). However, the output that I actaully want is a new matrix which keeps the corresponding values from the 2nd column of matrix A and B, along with the intercept values not just the intercept values which are spat out from the intersect function. So I end up with:

D = [2 8 10;
     2 3 2;
     1 2 1]

The above is a simplified example but I want to be able to apply it to a dataset with thousands of rows.

Answer 1

[Stephen23]

>> A = [2,4,6,8,10;2,3,5,3,2]
A =
    2    4    6    8   10
    2    3    5    3    2
>> B = [2,3,5,8,10;1,2,2,2,1]
B =
    2    3    5    8   10
    1    2    2    2    1
>> [V,X,Y] = intersect(A(1,:),B(1,:));
>> D = [V;A(2,X);B(2,Y)]
D =
    2    8   10
    2    3    2
    1    2    1

[Alex Hughes]

Apologies, I was rushing for a meeting and got my rows and columns mixed up! I meant to set up the two input matris like this:

A = [2 2; 4 3; 6 5; 8 3; 10 2]

B = [2 1; 3 2; 5 2; 8 2; 10 1]

To give the same output as before:

C = [2 2 1; 8 3 2; 10 2 1]

[Stephen23]

>> A = [2,2;4,3;6,5;8,3;10,2]
A =
    2    2
    4    3
    6    5
    8    3
   10    2
>> B = [2,1;3,2;5,2;8,2;10,1]
B =
    2    1
    3    2
    5    2
    8    2
   10    1
>> [V,X,Y] = intersect(A(:,1),B(:,1));
>> D = [V,A(X,2),B(Y,2)]
D =
    2    2    1
    8    3    2
   10    2    1

[Alex Hughes]

This works great my on data. Thanks.