I have two big matrices A and B with diffrent dimensions.I want to order the rows of matrix B with respect to rows of the matrix A. and add the rows with values 0 to matrix B, if that row is not exist in B but in A

Here is the reproduceable example and expected output:

A<-matrix(c(1:40), ncol=8)
rownames(A)<-c("B", "A", "C", "D", "E")

> A
  [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
B    1    6   11   16   21   26   31   36
A    2    7   12   17   22   27   32   37
C    3    8   13   18   23   28   33   38
D    4    9   14   19   24   29   34   39
E    5   10   15   20   25   30   35   40

> B<-matrix(c(100:108),ncol=3)
 rownames(B)<-c("A", "E", "C")

> B
  [,1] [,2] [,3]
A  100  103  106
E  101  104  107
C  102  105  108

Here is the Expected output :

>B
      [,1] [,2] [,3]
    B    0    0    0
    A  100  103  106
    C  102  105  108
    D    0    0    0
    E  101  104  107
    > 

Would someone help me to implement this in R ?