If matrix `A=[(3,2,-1),(-4,-1,-6)]`, then additive inverse of A is :

Options

A. `[(-3,-2,1),(4,1,6)]`
B. `[(6,4,-12),(8,2,12)]`
C. `[(0,0,0),(0,0,0)]`
D. `[(3,2,-1),(4,-1,-6)]`

Answer

To find the additive inverse of the matrix \( A = \begin{pmatrix} 3 & 2 & -1 \\ -4 & -1 & -6 \end{pmatrix} \), we follow these steps:

### Step 1: Understand the concept of additive inverse
The additive inverse of a matrix \( A \) is another matrix \( B \) such that when \( A \) and \( B \) are added together, they yield the zero matrix (null matrix). Mathematically, this can be expressed as:
\[ A + B = 0 \]
This implies that:
\[ B = -A \]

### Step 2: Calculate the additive inverse
To find the additive inverse of matrix \( A \), we need to negate each element of \( A \).

Given:
\[ A = \begin{pmatrix} 3 & 2 & -1 \\ -4 & -1 & -6 \end{pmatrix} \]

The additive inverse \( -A \) is calculated as follows:
\[ -A = \begin{pmatrix} -3 & -2 & 1 \\ 4 & 1 & 6 \end{pmatrix} \]

### Step 3: Write the final answer
Thus, the additive inverse of the matrix \( A \) is:
\[ -A = \begin{pmatrix} -3 & -2 & 1 \\ 4 & 1 & 6 \end{pmatrix} \]