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Find A=[[10,-9,-12],[7,-12,11],[-10,10,3]], |A^2|

Solution:
Your problem `->` A=[[10,-9,-12],[7,-12,11],[-10,10,3]], |A^2|


`A^2`=`A×A`=
`10``-9``-12`
`7``-12``11`
`-10``10``3`
×
`10``-9``-12`
`7``-12``11`
`-10``10``3`


=
`10×10-9×7-12×-10``10×-9-9×-12-12×10``10×-12-9×11-12×3`
`7×10-12×7+11×-10``7×-9-12×-12+11×10``7×-12-12×11+11×3`
`-10×10+10×7+3×-10``-10×-9+10×-12+3×10``-10×-12+10×11+3×3`


=
`100-63+120``-90+108-120``-120-99-36`
`70-84-110``-63+144+110``-84-132+33`
`-100+70-30``90-120+30``120+110+9`


=
`157``-102``-255`
`-124``191``-183`
`-60``0``239`


`A^2` = 
`10``-9``-12`
`7``-12``11`
`-10``10``3`
2
 = 
`157``-102``-255`
`-124``191``-183`
`-60``0``239`


`|A^2|` = 
 `157`  `-102`  `-255` 
 `-124`  `191`  `-183` 
 `-60`  `0`  `239` 


 =
 `157` × 
 `191`  `-183` 
 `0`  `239` 
 `+102` × 
 `-124`  `-183` 
 `-60`  `239` 
 `-255` × 
 `-124`  `191` 
 `-60`  `0` 


`=157 xx (191 × 239 - (-183) × 0) +102 xx (-124 × 239 - (-183) × (-60)) -255 xx (-124 × 0 - 191 × (-60))`

`=157 xx (45649 +0) +102 xx (-29636 -10980) -255 xx (0 +11460)`

`=157 xx (45649) +102 xx (-40616) -255 xx (11460)`

`= 7166893 -4142832 -2922300`

`=101761`







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