lem #7: A matrix 4 is called self-inverse if A = A. Which of the following statements are always true? O If A and B are both self-inverse n × n matrices then A+B is also self-inverse. (11) If A and B are both self-inverse 80 × 80 matrices, then the matrix AB is also self-inverse. (111) If A is self-inverse then -4 is also self-inverse where k is any nonzero constant. (A) (1) only (B) all of them (C) (1) and (i1) only (D) (ii) and (iii) only (E) none of them (F) (11) only (G) (iii) only (H) (i) and (iii) only

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 1SE: In a previous section, we showed that matrix multiplication is not commutative, that is, ABBA in...
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Problem #7: A matrix A is called self-inverse if A:
= A. Which of the following statements are always true?
1) If A and B are both self-inverse n × n matrices then A+B is also self-inverse.
(11) If A and B are both self-inverse 80 × 80 matrices, then the matrix AB is also self-inverse.
(111) If A is self-inverse then ÷4 is also self-inverse where k is any nonzero constant.
(A) (1) only (B) all of them (C) (1) and (ii) only (D) (ii) and (iii) only (E) none of them (F) (i11) only
(G) (iii) only (H) (i) and (iii) only
Transcribed Image Text:Problem #7: A matrix A is called self-inverse if A: = A. Which of the following statements are always true? 1) If A and B are both self-inverse n × n matrices then A+B is also self-inverse. (11) If A and B are both self-inverse 80 × 80 matrices, then the matrix AB is also self-inverse. (111) If A is self-inverse then ÷4 is also self-inverse where k is any nonzero constant. (A) (1) only (B) all of them (C) (1) and (ii) only (D) (ii) and (iii) only (E) none of them (F) (i11) only (G) (iii) only (H) (i) and (iii) only
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