Let A is a matrix of order `100xx 50 and ` B is matrix of order ` 50xx 75` and AB =C find the order of c

Options

A. 80
B. 50
C. 20
D. 10

Answer

To find the order of the matrix \( C \) resulting from the product of matrices \( A \) and \( B \), we follow these steps:

### Step 1: Identify the orders of matrices \( A \) and \( B \)
- Matrix \( A \) has an order of \( 100 \times 50 \).
- Matrix \( B \) has an order of \( 50 \times 75 \).

### Step 2: Check the compatibility for multiplication
- For the product of two matrices \( A \) (of order \( m \times n \)) and \( B \) (of order \( n \times p \)) to be defined, the number of columns in \( A \) (which is \( n \)) must equal the number of rows in \( B \) (which is also \( n \)).
- Here, the number of columns in \( A \) is \( 50 \) and the number of rows in \( B \) is \( 50 \). Since these are equal, the multiplication \( AB \) is defined.

### Step 3: Determine the order of the resulting matrix \( C \)
- The order of the resulting matrix \( C \) from the product \( AB \) will be given by the number of rows of \( A \) and the number of columns of \( B \).
- Matrix \( A \) has \( 100 \) rows and matrix \( B \) has \( 75 \) columns.
- Therefore, the order of matrix \( C \) is \( 100 \times 75 \).

### Conclusion
The order of matrix \( C \) is \( 100 \times 75 \).

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