If a matrix A is 3x2, what is the order of its transpose A^T?a.2x3b.3x3c.3x2d.2x2

1. ### Break Down the Problem

We need to determine the order (dimensions) of the transpose of matrix $A$, which is a $3 \times 2$ matrix.

2. ### Relevant Concepts

The order of the transpose of a matrix $A$ with dimensions $m \times n$ is $n \times m$.

3. ### Analysis and Detail

1. Given that the matrix $A$ has dimensions $3 \times 2$:

   • $m = 3$
   • $n = 2$

2. To find the dimensions of the transpose $A^T$:

   • The new dimensions become $n \times m$.
   • Therefore, $A^T$ will have dimensions $2 \times 3$.

4. ### Verify and Summarize

The transpose of a $3 \times 2$ matrix is correctly calculated, confirming that the dimensions are $2 \times 3$.

Final Answer

The order of the transpose $A^T$ is $2 \times 3$. Thus, the correct option is a. 2x3.