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a,b,c are matrices a + b + c = b + a + c true or false

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2 Answers

Lets look at and example. Assume for a moment that

A=[a1, a2],  B=[b1, b2] where each element is a real number. 

Remember that matrix addition is done component wise.

Thus A+B = [a1, a2]+[b1, b2] = [a1+b1, a2+b2]

and B+A = [b1, b2]+[a1, a2] = [b1+a1, b2+a2]

so the question is, is a1+b1=b1+a1 and a2+b2=b2+a2

Remember the commutative property of addition.

Can you expand this example to fit your problem?

Comments

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Good answer by Samuel. You should also ask yourself: in matrix multiplication is AB = BA? And the general answer is no.