Auto detect the matrix type Example-2

2. Auto detect the matrix type ?
`[[2,3,1],[0,5,6],[1,1,2]]`

Solution:

A matrix, in which number of rows and number of columns are equal, is called a square matrix.

`A`

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

The number of rows(3) and number of columns(3) are equal, So `A` is a square matrix

A square matrix `A`, such that `|A| != 0`, is called nonsingular matrix.

`A`

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

`|A|`

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

`2`

	`5`	`6`
	`1`	`2`

`-3`

	`0`	`6`
	`1`	`2`

`+1`

	`0`	`5`
	`1`	`1`

`=2 xx (5 × 2 - 6 × 1) -3 xx (0 × 2 - 6 × 1) +1 xx (0 × 1 - 5 × 1)`

`=2 xx (10 -6) -3 xx (0 -6) +1 xx (0 -5)`

`=2 xx (4) -3 xx (-6) +1 xx (-5)`

`= 8 +18 -5`

`=21`

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

This material is intended as a summary. Use your textbook for detail explanation.
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2. Example-2