Inverse of [2, 4; 1, 2]

Step by step

The question

Question: find the inverse of A.

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.

1 Find the determinant

First we need D, the determinant of A.

So D = 2 × 2 − 1 × 4.

2 times 2 is 4.

1 times 4 is 4.

4 minus 4 is 0.

So D = 0.

D is 0.

We would have to divide by 0, and that is impossible.

So A has no inverse.