Exercise 3.4 answers: Matrices
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Exercise 3.4
1 question · page 69 of the book
Question 1
“Matrices A and B will be inverse of each other only if” · p. 69
Open NCERT p. 69Matches NCERT’s answer
- By definition, A and B are inverses of each other when both products give the identity matrix: AB = I and BA = I.
- (A) AB = BA is not enough. Take A = 2I and B = 3I (order 2): AB = BA = 6I, which is not I, so they are not inverses. (Inverse pairs do have AB = BA, but that alone does not make them inverses.)
- (B) AB = BA = 0 can never work: the definition needs AB = I, and the zero matrix is not I.
- (C) AB = 0, BA = I can never work either: again the definition needs AB = I, not 0.
- (D) AB = BA = I is exactly the definition of an inverse pair.
AnswerAB = BA = I — option (D).
Watch this explained “The definition demands two products”, 0:50 into What it takes to be an inverse, and why there can only ever be one
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