Problem 10. Let [a b] c d Show that A is invertible if ad - cb / 0 by letting and showing that AB = BA= I2. B = A = 1 d ad cb -C 이 a

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Problem 10. Let
A =
с
Show that A is invertible if ad - cb / 0 by letting
1
d
B-ad-co [ca]
=
cb-c
and showing that AB = BA = I₂.
-1
Notice: B is then A-¹ and this problem gives us a formula for the inverse of a 2×2 matrix,
so long as ad — bc ‡ 0. This is a very important formula and should be memorized.
Transcribed Image Text:Problem 10. Let A = с Show that A is invertible if ad - cb / 0 by letting 1 d B-ad-co [ca] = cb-c and showing that AB = BA = I₂. -1 Notice: B is then A-¹ and this problem gives us a formula for the inverse of a 2×2 matrix, so long as ad — bc ‡ 0. This is a very important formula and should be memorized.
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