Given :
[tex]A = \begin{pmatrix}1&2\\ \:-1&4\end{pmatrix}\\\\\\B = \begin{pmatrix}3&2\\ \:\:4&\frac{1}{2}\end{pmatrix}[/tex]
Calculate :
i. AB
II. BA
III. What do you notice ?

Respuesta :

[tex]\\ \sf\longmapsto A=(1-4)-(2+1)[/tex]

[tex]\\ \sf\longmapsto A=-3-3[/tex]

[tex]\\ \sf\longmapsto A=-6[/tex]

[tex]\\ \sf\longmapsto B=(3-\dfrac{1}{2})-(2-4)[/tex]

[tex]\\ \sf\longmapsto B=\left(\dfrac{5}{2}\right)+2[/tex]

[tex]\\ \sf\longmapsto B=\dfrac{5+4}{2}[/tex]

[tex]\\ \sf\longmapsto B=\dfrac{9}{2}[/tex]

Now

[tex]\\ \sf\longmapsto AB=-6\times \dfrac{9}{2}[/tex]

[tex]\\ \sf\longmapsto AB=-3(9)[/tex]

[tex]\\ \sf\longmapsto AB=-27[/tex]

BA

[tex]\\ \sf\longmapsto \dfrac{9}{2}\times (-6)[/tex]

[tex]\\ \sf\longmapsto 9(-3)[/tex]

[tex]\\ \sf\longmapsto -27[/tex]

Observed:-

[tex]\\ \sf\longmapsto AB=BA[/tex]