A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose ?

Options

A. 64
B. 36
C. 32
D. 4

Explanation

To find the determinant of the transpose of a square matrix \( A \) of order 3, given that the determinant of \( A \) is 4, we can follow these steps:

### Step 1: Understand the properties of determinants
The determinant of a matrix has certain properties, one of which is that the determinant of a matrix and its transpose are equal. This means that for any square matrix \( A \), the following holds true:
\[ \text{det}(A) = \text{det}(A^T) \]

### Step 2: Apply the property to the given matrix
Since we are given that the determinant of matrix \( A \) is:
\[ \text{det}(A) = 4 \]
we can directly apply the property from Step 1.

### Step 3: Conclude the determinant of the transpose
Using the property we identified, we can state:
\[ \text{det}(A^T) = \text{det}(A) = 4 \]

### Final Answer
Thus, the determinant of the transpose of matrix \( A \) is:
\[ \text{det}(A^T) = 4 \]

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