The statement is false.

To understand why, we need to recall the following property of determinants:

• If $A$ is an $n \times n$ matrix and $c$ is a scalar, then:

$\det(cA) = c^n \det(A)$

In this case, $A$ is a 2x2 matrix, so $n = 2$.

The determinant of $5A$, where $A$ is a 2x2 matrix, is:

$\det(5A) = 5^2 \cdot \det(A) = 25 \cdot \det(A)$

Given that $\det(A) = 3$, we have:

$\det(5A) = 25 \cdot 3 = 75$

So, the correct value of $\det(5A)$ is 75, not 70. Therefore, the statement is false.

Would you like further clarification or have any questions? Here are some related questions:

1. How does the scalar multiplication property of determinants work for matrices of different sizes?
2. What is the determinant of a matrix for different orders (e.g., 3x3, 4x4)?
3. How do we calculate the determinant of a 3x3 matrix using cofactor expansion?
4. What are the properties of determinants related to matrix inverses?
5. How do you calculate the determinant of a matrix when it's in triangular form?

Tip: Always remember that for a scalar $c$ and an $n \times n$ matrix, $\det(cA) = c^n \det(A)$, which is key when dealing with scaled matrices.