Removing rows of a matrix based on rows of another matrix!

Imagine I have two matrices with different sizes (let's say 6x2 and 5x2) as follows:

A = [47 10;
29 10;
23 10;
34 10;
12 10;
64 10];

B = [23 20;
12 20;
54 20
47 20;
31 20];

I need to compare A(:,1) with B(:,1) and delete the rows in matrix A whose first-column-element is different from matrix B's first-column-element (so my focus is only on first columns of the matrices). So I should eventually get something like this:

A = [47 10;
12 10;
23 10];

as "47", "12", and "23" are the only first-column-elements in A that also exist in B! I have written this but I get the error "Matrix dimensions must agree."!

TF = A(:,1) ~= B(:,1);
A(TF,:) = [];

Any ideas how I could fix this?

Answer 1

[Birdman]

A=A(ismember(A(:,1),B(:,1)),:)

Answer 2

[Steven Lord]

Since it doesn't seem like ordering matters [you don't require A(n, 1) to match B(n, 1) as long as it matches some element in B(:, 1)] use the ismember function.