Question

What is the inverse of this matrix?

[
1
1/2

0 −
1/4

]

Multiple choice question.

A)
[
3 0 −2
4 −9 −5
]


B)
[
1 2
0 −4
]


C)
[
2 4
−1 0
3 −1
]


D)
not possible

Answer 1

The matrix is A = [[1, 1/2],[0, −1/4]]. Its determinant = 1·(−1/4) − (1/2)·0 = −1/4, so invertible.

A^{-1} = (1/det)·[[d, −b],[−c, a]] = (−4)·[[-1/4, −1/2],[0, 1]] = [[1, 2],[0, −4]].

So answer B.