What is density matrix of one on two entangled qubits?

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The discussion centers on the density matrix of a single qubit from a system of two entangled qubits, A and B. The entangled state is represented as c1 * |A0> * |B0> + c2 * |A1> * |B1>, where c1 and c2 are complex coefficients satisfying |c1|^2 + |c2|^2 = 1. The density matrix for the first qubit is confirmed to be a 2x2 matrix, specifically |c1|^2 * |A0> * * PREREQUISITES

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Let we have two qubits A and B. First qubit has eigenstates |A0> and |A1>, and second has |B0> and |B1>.

Let them be in the entangled state, described with vector

c1 * |A0> * |B0> + c2 * |B0> * |B1>|

where c1 and c2 are complex numbers with |c1|^2 + |c2|^2 = 1.

Then what is density matrix, describing only first qubit separately? Is this matrix 1x1 or 2x2?
 
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Is the correct answer is 1x1 matrix

|c1|^2 * |A0> * <A0| + |c2|^2 * |A1> * <A1|

?
 

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