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Question
State whether the following statement is True or False: If 𝐴 and 𝐵 are two square matrices of the same order, then A+B=B+A
State whether the following statement is True or False: If 𝐴 and 𝐵 are two square matrices of the same order, then A+B=B+A
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Solution
The correct option is B True
Given that 𝐴 and 𝐵 are both square matrices of same order. Addition of matrices 𝐴 and 𝐵 is defined as they have same order. Now, we know addition of elements is commutative i.e. a+p=p+a So, addition of matrix 𝐴 and 𝐵 is also commutative. i.e., A+B=B+A Hence, the given statement is true
Given that 𝐴 and 𝐵 are both square matrices of same order. Addition of matrices 𝐴 and 𝐵 is defined as they have same order. Now, we know addition of elements is commutative i.e. a+p=p+a So, addition of matrix 𝐴 and 𝐵 is also commutative. i.e., A+B=B+A Hence, the given statement is true
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