Question

Do the matrices have inverses? Justify your answer.

a. ????−2 6
−3 9
???? b. ????−2 6
3 9
????

Answer 1

a. No

b. Yes

Explanation:

as we know the inverse of the matrix is A⁻¹ = (adjA)/det(A)

If the determinant of the matrix is 0 then the inverse of that matrix does not exists.

For first matrix the determinant is

|A| =
`(-2*9)-(6*(-3))`

`=-18-(-18)\\=-18 + 18\\=0`

Hence the inverse of this matrix does not exists.

|B| =
`(-2*9)-(6*3)`

`-36`

Since the determinant of the matrix in the second option is non-zero .Hence it's inverse exists.