Qiskit CNOT-gate matrix mixup?

Question

In the qiskit textbook chapter 1.3.1 "The CNOT-Gate" it says that the matrix representation on the right is the own corresponding to the circuit shown above, with q_0 being the control and q_1 the target, but shouldn't this matrix representation be for the case of q_1 being the control and q_0 the target? This seems to be presented the other way round...or there seems to be something I am not quite getting yet.
Thanks so much :)
Quick edit: By "right" I am referring to this:

Egretta.Thula · Accepted Answer

Qiskit uses "little endian" bit ordering. That means, if A and B are $2 times 2$ unitary matrices then
$B otimes A$ (note the order) is equivalent to applying $A$ to first qubit and $B$ to second qubit.
Hence,
$$CNOT = I otimes P_0 + X otimes P_1$$
where
$$
P_0 = left( {begin{array}{*{20}{c}} 1&0  0&0 end{array}} right)
, P_1 = left( {begin{array}{*{20}{c}} 0&0  0&1 end{array}} right)
$$
If you do the matrix multiplication, you should get
$$CNOT = left( {begin{array}{*{20}{c}} 1&0&0&0  0&0&0&1  0&0&1&0  0&1&0&0 end{array}} right)$$

Mujtaba Sattar Anonto · Answer

Hi there. the Matrix for 0,1 is to represent Q[0] = 1 to be effective, right, so that I wrote & got the answer for the Coefficient to be |01> is 1 in the last column of the Density Matrix.
Consequently do note that the for CNOT for 1,0 to be effecive Q[1] must be one so i get the representation of the the co-efficient of |10> to be 1 as the the last column of the matrix.
Also my Dears, Please do kindly note that the Density Matrix column has direct Relationship with the State Specially the 1st & last column.

Qiskit CNOT-gate matrix mixup?

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