A= [2 3 0]

[4 1 6]
1. what is the additive inverse of A?

2. find 3A.

#1. just change the sign of all the elements of A.

#2. just multiply all the elements by 3.

J block kkgii

To find the answers to these questions, we need to understand what is meant by the additive inverse of a matrix and scalar multiplication.

1. The additive inverse of a matrix is a matrix that, when added to the original matrix, will result in the zero matrix. In other words, it is the matrix that cancels out the original matrix when added together.

To find the additive inverse of A, we need to negate each element in the matrix. Let's denote the additive inverse of A as -A:

-A = [-2 -3 0]
[-4 -1 -6]

So the additive inverse of A is:
-A = [-2 -3 0]
[-4 -1 -6]

2. Scalar multiplication is the process of multiplying each element in a matrix by a single scalar value. In this case, we want to find 3A, which means we need to multiply each element in A by 3.

3A = [3 * 2 3 * 3 3 * 0]
[3 * 4 3 * 1 3 * 6]

Simplifying the above expression, we get:
3A = [6 9 0]
[12 3 18]

So, 3A = [6 9 0]
[12 3 18]

To summarize:
1. The additive inverse of A is:
-A = [-2 -3 0]
[-4 -1 -6]

2. 3A = [6 9 0]
[12 3 18]