Show that B is the inverse of A. -6 9 18 40-4 - 1 1 2 1 -1 -1 A = STEP 1: Find AB. AB= X STEP 2: Find BA. BA = 1 0 0 1 5/3 -5/3 0 1 0 2 = 0 ↓1 -11/3 ↓ 1 3 1 -9 0 1 -12 -6 3 3 12 1 -2/3 4 5/3 0 ↓ 1 = I = I

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that B is the inverse of A.
-6
9 18
- 1
1
2
1
-1
-1
STEP 1: Find AB.
A =
AB=
X
STEP 2: Find BA.
BA
=
1
0
0
1
5/3
-5/3
0
1
0
2
=
0
↓1
-11/3
↓ 1
3
1
-9 0
1 -12 -6
0
3
3
12
1
-2/3
4
5/3
0
= I
= I
Transcribed Image Text:Show that B is the inverse of A. -6 9 18 - 1 1 2 1 -1 -1 STEP 1: Find AB. A = AB= X STEP 2: Find BA. BA = 1 0 0 1 5/3 -5/3 0 1 0 2 = 0 ↓1 -11/3 ↓ 1 3 1 -9 0 1 -12 -6 0 3 3 12 1 -2/3 4 5/3 0 = I = I
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