The mathematical statement seems simple.

It means the multiplication of variable A and B equals zero.

Though it seems simple and direct, mistake in understanding the implication of the zero exists.

When we say AB = 0, we indirectly (and logically) deduce that A = 0 or B = 0.

This deduction is with taken regardless of what the other variable is.

When we say A = 0, B can be anything since 0 multiply "anything" = 0.

This is true vice versa for B = 0.

But what if AB = 1? or AB = x?

This is where misconception of the "logically" deduction happens.

Many maths learners assumed that since AB = 0 indicated A = 0 or B = 0,

AB=1 indicated A = 1 or B = 1 also!

This is a grave and serious

*made.*

**mistake****AB= 1 does not imply A = 1 or B = 1 .**

If

**A = "1"**is true, then

**A**B = 1 means "

**1**" x B = 1, which is definitely false, as 1 x B = B!

Likewise when B= 1 is assumed.

Therefore the AB = 0 cannot be applied across the board to cover all else with the same deduction.

The equal to Zero has special meaning, and should not be confused with other number equated.

**In summary**: AB = 0 means A= 0 or B= 0 only if "= 0".

A little accurate understanding goes a long way.... in maths, especially.

:-)

## 2 comments:

Since you also discuss matrices here, I think you should emphasize here that A and B are numbers. Because of course if A and B are matrices then AB=0 doesn't imply that A=0 or B=0.

I recently came accross your blog and have been reading along. I thought I would leave my first comment. I dont know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often.

Kate

http://educationonline-101.com

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