# Check whether the following matrix is invertible or not: (1232-13123) - Mathematics and Statistics

Sum

Check whether the following matrix is invertible or not:

((1,2,3),(2,-1,3),(1,2,3))

#### Solution

Let A = ((1,2,3),(2,-1,3),(1,2,3))

Then, |A| = |(1,2,3),(2,-1,3),(1,2,3)|

= 1(- 3 - 6) - 2(6 - 3) + 3(4 + 1)

= - 9 - 6 + 15

= 0

∴ A is a singular matrix.

Hence, A-1 does not exist.

Concept: Elementry Transformations
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