Find `|adj(a)|` if |A|= 7 and A is a square matrix of order 3

Explanation

To find the value of \(|\text{adj}(A)|\) given that \(|A| = 7\) and \(A\) is a square matrix of order 3, we can follow these steps:

### Step 1: Understand the relationship between the determinant of a matrix and its adjoint.
The determinant of the adjoint of a matrix \(A\) is given by the formula:
\[ |\text{adj}(A)| = |A|^{n-1} \]
where \(n\) is the order of the matrix \(A\).

### Step 2: Identify the order of the matrix.
In this case, the matrix \(A\) is of order 3, so we have:
\[ n = 3 \]

### Step 3: Substitute the values into the formula.
Given that \(|A| = 7\), we can substitute this value into the formula:
\[ |\text{adj}(A)| = |A|^{n-1} = 7^{3-1} \]

### Step 4: Simplify the expression.
Now we simplify the exponent:
\[ |\text{adj}(A)| = 7^{2} = 49 \]

### Final Answer:
Thus, the value of \(|\text{adj}(A)|\) is:
\[ |\text{adj}(A)| = 49 \]

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