Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm not sure this should go in homework of here as this was a test question, but the question its self isn't a test question.

I got this question marked wrong, for the record.

Question

For each statement below, determine if the statement is true or false. If true, provide a proof, if false, provide a counterexample.

A.) If A is a nonzero matrix, and if AB = 0 (the zero matrix), then B = 0

Suppose [tex]A[/tex] has a inverse and[tex] B ≠ 0 [/tex]

Then,

[tex] A^{-1}AB = 0{A^-1}[/tex]

[tex]I_nB = 0[/tex]

Since Identity * B ≠ 0 unless B is the zero matrix, B must be zero.

However, the professor simply wrote false and then gave an example of how it was possible for the matrix to not be the zero matrix.

However, I clearly showed B can be zero.

So, the real question I'm asking is if this question was to be seen in any sense what is the context of the equal sign; in terms of any mathematics to make a statement false of true.

For example would this statement also be false..in terms of the question below.

For each statement below, determine if the statement is true or false. If true, provide a proof, if false, provide a counterexample.

Let f(x) = 4 and f(x) = x^2, then x = -2.

I would have to say false?

Because,

Let f(x) = 4 and f(x) = x^2, then x = -2 and x = 2.

Comments please, and rip it apart :D

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# What does this statement even mean?

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