1. is Nonsingular Matrix ?
`[[2,2,3],[4,5,6],[7,8,9]]`

Solution:

`A`

=

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

`|A|`

=

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

=

`2`   ×    `5`   `6`   `8`   `9`

`-2`   ×    `4`   `6`   `7`   `9`

`+3`   ×    `4`   `5`   `7`   `8`

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

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

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

`= -6 +12 -9`

`=-3`


Here, `|A| != 0`, so `A` is nonsingular matrix

---

2. is Nonsingular Matrix ?
`[[1,2,3],[4,5,6],[7,8,9]]`

Solution:

`A`

=

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

`|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` is a singular matrix

---

---