module matrix_module
implicit none

contains
  subroutine matrix_bits(a,b,c,a_t,n)
  implicit none
  integer, intent (in) :: n
  real, dimension (:,:), intent (in) :: a, b
  real, dimension (:,:), intent (out) :: c, a_t
  integer :: i, j, k
  real :: temp
! matrix multiplication c=ab
    do i = 1, n
      do j = 1, n
        temp = 0.0
        do k = 1, n
          temp = temp + a(i,k)*b(k,j)
        end do
        c(i,j) = temp
      end do
    end do
! calculate a_t transpose of a
! set a_t to be transpose matrix a
    do i = 1, n
      do j = 1, n
        a_t(i,j) = a(j,i)
      end do
    end do
  end subroutine matrix_bits
end module matrix_module

program ch2003
use matrix_module
implicit none
real, allocatable, dimension (:,:) :: one, two, three, one_t
integer :: i, n

  print *, 'input size of matrices'
  read *, n
  allocate (one(1:n,1:n))
  allocate (two(1:n,1:n))
  allocate (three(1:n,1:n))
  allocate (one_t(1:n,1:n))
  do i = 1, n
    print *, 'input row ', i, ' of one'
    read *, one(i,1:n)
  end do
  do i = 1, n
    print *, 'input row ', i, ' of two'
    read *, two(i,1:n)
  end do
  call matrix_bits(one,two,three,one_t,n)
  print *, ' matrix three:'
  do i = 1, n
    print *, three(i,1:n)
  end do
  print *, ' matrix one_t:'
  do i = 1, n
    print *, one_t(i,1:n)
  end do
end program ch2003