- #1

songoku

- 2,319

- 331

- Homework Statement
- Please see below

- Relevant Equations
- Matrix Multiplication

My attempt:

Let C =

$$\begin{pmatrix}

c_{11} & c_{12} & c_{13} \\

c_{21} & c_{22} & c_{23} \\

c_{31} & c_{32} & c_{33}

\end{pmatrix}$$

If C is multiplied by B, then:

1)

a

_{21}= c

_{21}. b

_{11}

0 = c

_{21}. b

_{11}##\rightarrow c_{21}=0##

2)

a

_{31}= c

_{31}. b

_{11}

0 = c

_{31}. b

_{11}##\rightarrow c_{31}=0##

3)

a

_{32}= c

_{32}. b

_{22}

0 = c

_{32}. b

_{22}##\rightarrow c_{32}=0##

But a

_{33}= c

_{31}. b

_{13}+ c

_{32}. b

_{23}+ c

_{33}. b

_{33}= 0, which contradicts the restriction from the question

So actually matrix C does not exist, not only invertible matrix C does not exist but also non - invertible matrix C can not exist.

Is this what the question wants? Or I am missing something?

Thanks