Question

Given :


`A = \begin{pmatrix}1&2\\ \:-1&4\end{pmatrix}\\\\\\B = \begin{pmatrix}3&2\\ \:\:4&(1)/(2)\end{pmatrix}`
Calculate :
i. AB
II. BA
III. What do you notice ?

Answer 1

`\\ \sf\longmapsto A=(1-4)-(2+1)`

`\\ \sf\longmapsto A=-3-3`

`\\ \sf\longmapsto A=-6`

`\\ \sf\longmapsto B=(3-(1)/(2))-(2-4)`

`\\ \sf\longmapsto B=\left((5)/(2)\right)+2`

`\\ \sf\longmapsto B=(5+4)/(2)`

`\\ \sf\longmapsto B=(9)/(2)`

Now

`\\ \sf\longmapsto AB=-6* (9)/(2)`

`\\ \sf\longmapsto AB=-3(9)`

`\\ \sf\longmapsto AB=-27`

BA

`\\ \sf\longmapsto (9)/(2)* (-6)`

`\\ \sf\longmapsto 9(-3)`

`\\ \sf\longmapsto -27`

Observed:-

`\\ \sf\longmapsto AB=BA`