`(A^(3))^(-1)=(A^(-1))^(3)`, where A is a square matrix and `|A|!=0`

Explanation

To determine whether the statement \((A^{3})^{-1} = (A^{-1})^{3}\) is true or false, we can use properties of matrix inverses. Here is a step-by-step solution:

### Step 1: Understand the properties of matrix inverses
We know that for any square matrix \(A\) (where \(|A| \neq 0\)), the inverse of a power of a matrix can be expressed as:
\[ (A^n)^{-1} = (A^{-1})^n \]
for any natural number \(n\).

### Step 2: Apply the property to the given expression
In our case, we have \(n = 3\). Therefore, we can apply the property:
\[ (A^{3})^{-1} = (A^{-1})^{3} \]

### Step 3: Conclude the validity of the statement
Since we have shown that \((A^{3})^{-1} = (A^{-1})^{3}\) holds true based on the property of matrix inverses, we conclude that the statement is indeed true.

### Final Answer:
The statement \((A^{3})^{-1} = (A^{-1})^{3}\) is **True**.