Question

Given `A=((-1, 2), (3, 4))` and `B=((-4, 3), (5, -2))`, how do you find `A^-1`?

Answer 1

`A^{-1}=((-2/5, 1/5),(3/10, 1/10))`.

Explanation:

There is a rule to calculate the inverse of a `2\times 2` matrix.
If we have a matrix `M` with components
`M=((a, b),(c, d))` the inverse is
`M^{-1}=1/(ad-bc)((d, -b),(-c, a))`.

We can apply this to the matrix `A` and obtain

`A^{-1}=1/(-1*4-2*3)((4,-2),(-3,-1))`
`=1/(-10)((4, -2),(-3, -1))`
`=((-4/10, 2/10),(3/10, 1/10))`
`=((-2/5, 1/5),(3/10, 1/10))`.

Unfortunately I do not understand what should be the role of B because to invert a matrix you don't need another matrix.