WEBVTT

1
00:00:00.000 --> 00:00:01.695
Here is the problem: [[2, 1], [1, 1]].

2
00:00:02.145 --> 00:00:04.943
Find the inverse of a 2 times 2 matrix.

3
00:00:05.743 --> 00:00:07.914
Check that the determinant is non-zero.

4
00:00:08.364 --> 00:00:12.811
Swap a and d, negate b and c, divide by the determinant.

5
00:00:13.261 --> 00:00:16.872
Check: A times A to the power minus 1 equals I.

6
00:00:17.672 --> 00:00:22.037
So the answer is A to the power minus 1 equals [[1, negative 1], [-1, 2]].

7
00:00:22.487 --> 00:00:27.630
The determinant is 1, so A is invertible. Every entry of the inverse is exact.

8
00:00:28.430 --> 00:00:32.737
Multiplying A by the result gives the identity matrix exactly.