If |A| = 8, where A is square matrix of order 3, then what is |adj A| equal to ?

Options

A. 16
B. 24
C. 64
D. 512

Explanation

To find the value of |adj A| given that |A| = 8 and A is a square matrix of order 3, we can use the following steps:

### Step 1: Understand the relationship between the determinant of a matrix and its adjoint.
The determinant of the adjoint of a matrix A, denoted as |adj A|, is related to the determinant of A by the formula:
\[ |adj A| = |A|^{n-1} \]
where n is the order of the matrix A.

### Step 2: Identify the order of the matrix A.
In this case, we are given that A is a square matrix of order 3. Therefore, n = 3.

### Step 3: Substitute the values into the formula.
We know that |A| = 8 and n = 3. Now we can substitute these values into the formula:
\[ |adj A| = |A|^{n-1} = |A|^{3-1} = |A|^{2} \]
\[ |adj A| = 8^{2} \]

### Step 4: Calculate the value.
Now we calculate \(8^2\):
\[ 8^2 = 64 \]

### Conclusion:
Thus, the value of |adj A| is 64.

### Final Answer:
\[ |adj A| = 64 \]

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