Make true all the false rows of a column of a matrix which are in between the first true and the last true row

The first true element of column 1 of matrix a is at row 2. The last true element of column 1 of matrix a is at row 9. I want to get a matrix b whose 1st column will start with false, from row 2 to row 9 will b true and row 10 will be false. Likewise, I want to do the same for the rest of the columns of matrix a.

Example:

a =[

       0     0     1     0
       1     0     0     0
       1     0     0     1
       1     0     0     1
       1     1     1     0
       0     0     0     1
       1     1     1     0
       0     1     1     0
       1     0     0     0
       0     0     0     1];

b =[

       0     0     1     0
       1     0     1     0
       1     0     1     1
       1     0     1     1
       1     1     1     1
       1     1     1     1
       1     1     1     1
       1     1     1     1
       1     0     0     1
       0     0     0     1];

Answer 1

[Andrei Bobrov]

b = cumsum(a)&flipud(cumsum(flipud(a)))

[Giorgos Papakonstantinou]

I am impressed! I must thank you!