Step by step
The question
Question: find the inverse of A.
A = [3, 6; −1, −2]
The inverse of A is written A⁻¹.
A times its inverse gives I: 1s down the diagonal, 0s elsewhere.
Times I changes nothing, like times 1.
A × A−1 = I, I = [1, 0; 0, 1]
1 Find the determinant
First we need D, the determinant of A.
D = |3, 6; −1, −2|
So D = 3 × (−2) − (−1 × 6).
D = 3 × (−2) − (−1 × 6)
3 times (−2) is −6.
−1 times 6 is −6.
D = −6 − (−6)
Taking away a negative is adding: −6 + 6.
−6 − (−6) = −6 + 6
−6 minus (−6) is 0.
So D = 0.
D = 0
D is 0.
We would have to divide by 0, and that is impossible.
So A has no inverse.
D = 0: no inverse
Answer
D = 0: no inverse