If order of matrix A is `2xx3` and order of matrix B is `3xx5`, then order of matrix `B'A'` is :

Options

A. `5xx2`
B. `2xx5`
C. `5xx3`
D. `3xx2`

Answer

To find the order of the matrix \( B'A' \) where \( A \) and \( B \) have given orders, we can follow these steps:

### Step 1: Identify the orders of matrices A and B
- The order of matrix \( A \) is \( 2 \times 3 \).
- The order of matrix \( B \) is \( 3 \times 5 \).

### Step 2: Determine the orders of the transposes of matrices A and B
- The order of the transpose of matrix \( A \) (denoted as \( A' \)) will be the reverse of the order of \( A \). Therefore, the order of \( A' \) is \( 3 \times 2 \).
- The order of the transpose of matrix \( B \) (denoted as \( B' \)) will also be the reverse of the order of \( B \). Therefore, the order of \( B' \) is \( 5 \times 3 \).

### Step 3: Find the order of the product \( B'A' \)
- Now we need to multiply \( B' \) and \( A' \).
- The order of \( B' \) is \( 5 \times 3 \) and the order of \( A' \) is \( 3 \times 2 \).
- When multiplying two matrices, the number of columns of the first matrix must equal the number of rows of the second matrix. Here, \( B' \) has 3 columns and \( A' \) has 3 rows, so they can be multiplied.

### Step 4: Determine the order of the resulting matrix
- The order of the resulting matrix from the multiplication \( B'A' \) will be determined by the number of rows of the first matrix and the number of columns of the second matrix.
- Therefore, the order of \( B'A' \) will be \( 5 \times 2 \).

### Conclusion
The order of the matrix \( B'A' \) is \( 5 \times 2 \).

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