1. Find `A^-1` ...
`A=[[1,2],[4,5]]`

Solution:

`|A|`

=

`1`   `2`   `4`   `5`

`=1 × 5 - 2 × 4`

`=5 -8`

`=-3`

`Adj(A)`

=

Adj `1` `2` `4` `5`

=	`+(5)` `-(4)` `-(2)` `+(1)` T

=	`5` `-4` `-2` `1` T

=	`5` `-2` `-4` `1`

`"Now, "A^(-1)=1/|A| × Adj(A)`

=

`1/(-3)` ×

`5` `-2` `-4` `1`

=	`-1.6667` `0.6667` `1.3333` `-0.3333`

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2. Find `A^-1` ...
`A=[[1,2,3],[4,5,6],[7,8,9]]`

Solution:

`|A|`

=

`1`   `2`   `3`   `4`   `5`   `6`   `7`   `8`   `9`

=

`1`   ×    `5`   `6`   `8`   `9`

`-2`   ×    `4`   `6`   `7`   `9`

`+3`   ×    `4`   `5`   `7`   `8`

`=1 xx (5 × 9 - 6 × 8) -2 xx (4 × 9 - 6 × 7) +3 xx (4 × 8 - 5 × 7)`

`=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)`

`=1 xx (-3) -2 xx (-6) +3 xx (-3)`

`= -3 +12 -9`

`=0`


`Here, |A|=0, " So " (A)^(-1)" is not possible."`

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