Mark each of the following statement true or false: If A and B are matrices such that AB = O and $A\ne O$ , then B = O.

ediculeN
2021-01-13
Answered

Mark each of the following statement true or false: If A and B are matrices such that AB = O and $A\ne O$ , then B = O.

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ensojadasH

Answered 2021-01-14
Author has **100** answers

Step 1

Given statement,

If A and B are matrices such that AB = O and$A\ne O$ , then B = O.

Step 2

Take A and B to be two matrices

$A=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]\ne 0\text{and}B=\left[\begin{array}{cc}0& 0\\ 1& 0\end{array}\right]$

$AB=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{cc}0& 0\\ 1& 0\end{array}\right]$

$AB=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\text{and}A=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]\ne 0$

But B is non Zero.

Therefore, the given statement is false.

Given statement,

If A and B are matrices such that AB = O and

Step 2

Take A and B to be two matrices

But B is non Zero.

Therefore, the given statement is false.

Jeffrey Jordon

Answered 2022-01-23
Author has **2313** answers

Answer is given below (on video)

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