Question

2. Let A be a 3 x 3 matrix such that det(A)= -4. Find det(3A)

Answer 1

The value of det (3A) is -108.

Explanation:

If M is square matrix of order n x n, then

`|kA|=k^n|A|`

Let as consider a matrix A or order 3 x 3. Using the above mentioned property of determinant we get

`|kA|=k^3|A|`

We need to find the value of det(3A).

`|3A|=3^3|A|`

`|3A|=27|A|`

It is given that the det(A)= -4. Substitute |A|=-4 in the above equation.

`|3A|=27(-4)`

`|3A|=-108`

Therefore the value of det (3A) is -108.