If, we are given with a matrix then how can we find its additive inverse?
I will explain it with the help of example. You first need to know general definition of additive inverse in order to understand additive inverse of matrix.
Additive inverse of any given real number is the number which when added to the given real number results zero. For example , what is the additive inverse of integer 5. The additive inverse of 5 is -5 because 5+(-5) =0. Similarly, additive inverse of -6 is 6 because -6+6=0.
To find additive inverse of a given matrix A, we need to find a matrix which when added to the given matrix produces null matrix or zero matrix. To get additive inverse of given matrix, we just need to multiply each element of matrix with -1. When, we multiply each element of matrix with -1, it becomes equal to -A. Hence, A+(-A) becomes equal to 0 where 0 is a null matrix. It satisfies basic definition of additive inverse.
For example, We have a question:
Find additive inverse of matrix
We just multiply each element of matrix A with -1. We get matrix equal to .
We have already learnt how to add matrices. When we add A and (-A),
, we get a null matrix.
It satisfies definition of additive Inverse. Hence, to find additive inverse of any matrix, we just multiply each element of matrix with -1.