Question

If the sum of two matrices A and B is zero matrix, then A and B are said to be

Answer 1

Step-by-step explanation:

Given that: If the sum of two matrices A and B is zero matrix, then A and B are said to be?

Solution:

If two matrix A and B are not null matrix but sum of both matrix are a Null matrix,

Then A and B are called Additive Inverse of each other.

Let us take one example for better understanding

$A=\left[\begin{array}{cc}1&-2\\3&4\\\end{array}\right]$

and matrix B

$B=\left[\begin{array}{cc}-1&2\\-3&-4\\\end{array}\right]$

As one can easily see A and B both are not Null matrix

Add both A and B

$A+B=\left[\begin{array}{cc}1-1&-2+2\\3-3&4-4\\\end{array}\right]$

$A+B=\left[\begin{array}{cc}0&0\\0&0\\\end{array}\right]$

Thus, A+B is a Null matrix.

Thus,

A and B are additive inverse of each other.

Hope it helps you.