Question 3 Recall that M2 (R) denotes the set of 2 x 2 real matrices, and that if then det A = ad - bc. = a b A-[22]. C d 3/6 [3.1] Prove that the matrix multiplication on M2 (R) is associative. [3.2] Prove that if A, B E M2(R), then det (AB) = (det A)(det B).
Question 3 Recall that M2 (R) denotes the set of 2 x 2 real matrices, and that if then det A = ad - bc. = a b A-[22]. C d 3/6 [3.1] Prove that the matrix multiplication on M2 (R) is associative. [3.2] Prove that if A, B E M2(R), then det (AB) = (det A)(det B).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....
Question
![Question 3 Recall that M2 (R) denotes the set of 2 x 2 real matrices, and that if
then det A = ad - bc.
=
a
b
A-[22].
C
d
3/6
[3.1] Prove that the matrix multiplication on M2 (R) is associative.
[3.2] Prove that if A, B E M2(R), then det (AB) = (det A)(det B).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f638b0e-3266-4f7b-abd5-416eb3233ddf%2F36af4e00-714e-4845-96a6-676053026741%2Fdh5dn1s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3 Recall that M2 (R) denotes the set of 2 x 2 real matrices, and that if
then det A = ad - bc.
=
a
b
A-[22].
C
d
3/6
[3.1] Prove that the matrix multiplication on M2 (R) is associative.
[3.2] Prove that if A, B E M2(R), then det (AB) = (det A)(det B).
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