The substraction of a matrix B may be considered as the addition of the matrix (-1) B. Dose the commutative law of addition permit us to atate that A - B = B - A? If not, how would you correct the statement?

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Mathematics

Rocket

22 June, 20:12

The substraction of a matrix B may be considered as the addition of the matrix (-1) B. Dose the commutative law of addition permit us to atate that A - B = B - A? If not, how would you correct the statement?

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Sutton · Answer 1

Answer: The corrected statement is A - B = - B + A.

Step-by-step explanation: Given that the subtraction of a matrix B may be considered as the addition of the matrix (-1) B.

We are given to check whether the commutative law of addition permit us to state that A - B = B - A.

If not, We are to correct the statement.

If the subtraction A - B is considered a the addition A + (-B), then the commutative law should be stated as follows:

A + (-B) = (-B) + A.

That is, A - B = - B + A.

Thus, the corrected statement is A - B = - B + A, not B - A.