reduce matrix

I am trying to reduce the dimension of matrix by removing zero elements and creating a sub-matrix.

For example:

A= [1,0,0,3;  0,1,2,0; 0,0,3,5]

then the new matrix B would be:

B= [1,3;1,2;3,5]

There are the same number of zero elements in each row of A so dimension of B will not be a problem. Is there a straightforward way to do this in R without writing a function using loops etc?

Any help or suggestions would be appreciated!

Thanks