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Translation of the text:
"Matrix B is called the ... of matrix A, and the transition from A to B is called transposition if the elements of each row of matrix A are written in the same order in the columns of matrix B."

**Answer:**
Matrix B is called the **transpose** of matrix A. The transition from matrix A to matrix B is known as **transposition** when the elements of each row of matrix A are written in the same order as the elements of the columns of matrix B.

Would you like more details or have any questions about matrix transposition? Here are some related questions:

1. What is the definition of a transpose matrix in mathematical terms?
2. How does transposition affect the properties of a matrix, such as its determinant?
3. Can transposition change the rank of a matrix?
4. What are the practical applications of matrix transposition in fields like computer science or physics?
5. How do you calculate the transpose of a 3x3 or larger matrix?

**Tip:** When transposing a matrix, the dimensions of the matrix change from \( m \times n \) to \( n \times m \), where \( m \) is the number of rows and \( n \) is the number of columns.

Matrix B is called the ... of matrix A, and the transition from A to B is called transposition if the elements of each row of matrix A are written in the same order in the columns of matrix B.

Understand matrix transposition, where matrix B is the transpose of matrix A. The transition from A to B involves writing each row of A into the columns of B. This concept is essential in linear algebra and has applications in computer science, physics, and more.

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