# Negative of a Matrix

We will discuss about Negative of a Matrix.

The negative of the matrix A is the matrix (-1)A, written as – A.

For example:

Let A = $$\begin{bmatrix} 12 & -17\\ -5 & 9 \end{bmatrix}$$.

Then –A = (-1) $$\begin{bmatrix} 12 & -17\\ -5 & 9 \end{bmatrix}$$ = $$\begin{bmatrix} -12 & 17\\ 5 & -9 \end{bmatrix}$$

Clearly, the negative matrix is obtained by changing the signs of each element.

Solved examples on Negative of a Matrix:

1. If A = $$\begin{bmatrix} 2 & 5\\ 1 & 3 \end{bmatrix}$$ then find the negative matrix of A.

Solution:

A = $$\begin{bmatrix} 2 & 5\\ 1 & 3 \end{bmatrix}$$

The negative matrix of A = -A

Now by changing the signs of each element of matrix A

We get $$\begin{bmatrix} -2 & -5\\ -1 & -3 \end{bmatrix}$$

Therefore, the negative matrix of A = -A = $$\begin{bmatrix} -2 & -5\\ -1 & -3 \end{bmatrix}$$.

2. If M = $$\begin{bmatrix} 5 & -1\\ -3 & 2 \end{bmatrix}$$ then find the negative matrix of M.

Solution:

M = $$\begin{bmatrix} 5 & -1\\ -3 & 2 \end{bmatrix}$$

The negative matrix of M = -M

Now by changing the signs of each element of matrix M

We get $$\begin{bmatrix} -5 & 1 \\ 3 & -2 \end{bmatrix}$$

Therefore, the negative matrix of A = -A = $$\begin{bmatrix} -5 & 1 \\ 3 & -2 \end{bmatrix}$$.

3. If I = $$\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}$$ then find -I.

Solution:

I = $$\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}$$

The negative matrix of I = -I

Now by changing the signs of each element of matrix M

We get $$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$

Therefore, the negative matrix of I = -I = $$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$.

Note: A + (-A) = 0; i.e., Sum a matrix and its negative matrix = 0.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

Feb 28, 24 04:07 PM

There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

2. ### Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

Feb 28, 24 01:43 PM

The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

3. ### Fraction as a Part of Collection | Pictures of Fraction | Fractional

Feb 27, 24 02:43 PM

How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

4. ### Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Feb 24, 24 04:11 PM

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…