PROPERTIES OF MATRIX ADDITION PRACTICE WORKSHEET

Question 1 :

then, verify that A + (B + C) = (A + B) + C.

Question 2 :

then verify:

(i) A + B = B + A

(ii) A + (- A) = O = (- A) + A

Question 3 :

then find the additive inverse of A.

Question 1 :

then, verify that A + (B + C) = (A + B) + C.

Solution :

Question 2 :

then verify:

(i) A + B = B + A

(ii) A + (- A) = O = (- A) + A

Solution :

(i) 

By finding the sum of matrices A and B, we get the value of A + B.

By finding the sum of matrices B and A, we get the value of B + A.

From the above steps, it is clear that

A + B  =  B + A. 

Matrix addition is commutative.

(ii)   By adding A and -A, we get the value of A + (-A).

By adding -A and A, we get the value of -A + A.

From the above steps, it is clear that 

-A + A  =  0 and A + (-A)  =  0

Question 3 :

then find the additive inverse of A.

Solution :

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