If A is an invertible square matrix of order `4`, then `|adjA|=`.......

Answer

To find the value of \(|\text{adj} A|\) for an invertible square matrix \(A\) of order \(4\), we can follow these steps:

### Step 1: Understand the properties of the adjoint of a matrix
The adjoint of a matrix \(A\), denoted as \(\text{adj} A\), is related to the determinant of \(A\). Specifically, for an \(n \times n\) matrix \(A\), the determinant of the adjoint is given by the formula:
\[ |\text{adj} A| = |A|^{n-1} \]
where \(n\) is the order of the matrix.

### Step 2: Identify the order of the matrix
In this case, the matrix \(A\) is given to be of order \(4\). Therefore, we have:
\[ n = 4 \]

### Step 3: Apply the formula for the determinant of the adjoint
Using the formula from Step 1, we can substitute \(n = 4\):
\[ |\text{adj} A| = |A|^{4-1} = |A|^3 \]

### Step 4: Consider the condition of invertibility
Since \(A\) is specified to be an invertible matrix, we know that:
\[ |A| \neq 0 \]
This implies that \(|A|^3\) will also be non-zero.

### Conclusion
Thus, the final result for the determinant of the adjoint of matrix \(A\) is:
\[ |\text{adj} A| = |A|^3 \]