If AB=C and matrices B and C are of order 17*25 then the order of matrix A is

Given that \( AB = C \) and the matrices \( B \) and \( C \) are of order \( 17 \times 25 \), we need to determine the order of matrix \( A \).

Let’s denote the order of matrix \( A \) as \( m \times n \).

Given:
- \( B \) is \( 17 \times 25 \)
- \( C \) is \( 17 \times 25 \)

Since matrix multiplication is defined, the number of columns of \( A \) must match the number of rows of \( B \). Therefore, if \( A \) is \( m \times n \), then \( n \) must be \( 17 \) (the number of rows of \( B \)).

The resulting matrix \( C \) after multiplication has the same number of rows as \( A \) and the same number of columns as \( B \). Therefore, \( m = 17 \) and \( 25 \) are the dimensions of \( C \).

Thus, the order of matrix \( A \) is:

\[
\text{Order of matrix } A = 25 \times 17
\]

Would you like more details or have any questions? Here are five related questions:

1. How do you determine the order of a product of two matrices?
2. What are the conditions for matrix multiplication to be defined?
3. Can the order of the resulting matrix differ from the original matrices? If so, how?
4. What happens if the matrices have incompatible dimensions for multiplication?
5. How does the associative property of matrix multiplication affect the result?

**Tip:** Always ensure the inner dimensions (the number of columns in the first matrix and the number of rows in the second matrix) match when multiplying matrices.

Understand how to determine the order of matrix A from the equation AB = C where matrices B and C are 17x25. Learn about matrix multiplication, dimensions, and the relationship between matrix sizes. Suitable for advanced high school students and anyone interested in matrix algebra.

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