Matrices A and B will be inverse of each other only if (A) AB=BA (B) AB=BA=0 (C) AB=0, BA=I (D) AB=BA=I.
Hint. Recall the exact definition of an inverse matrix from this chapter's Definition 6.
By definition, B is the inverse of A exactly when both products AB and BA equal the identity matrix I.
✦ (D) AB=BA=I
Solutions written by the tuition.in editorial team and checked against the NCERT Class 12 Mathematics textbook, Reprint 2026-27 (lemh103.pdf) — Exercise 3.1 (10 questions), Exercise 3.2 (22 questions), Exercise 3.3 (12 questions), Exercise 3.4 (1 question), plus the chapter's Miscellaneous Exercise (11 questions), 56 questions total. Exercise pages were rendered as 300dpi images throughout to read matrix bracket notation accurately, since raw text extraction badly garbled every matrix in the chapter. The old stub taught 'finding the inverse using elementary row/column operations' as a core section, but that method has been fully removed from the current edition — Section 3.7 only proves existence and uniqueness of an inverse, and Exercise 3.4 has shrunk from what older editions had down to a single leftover MCQ, confirmed by reading straight through the section with nothing about row-reducing a matrix anywhere in it. The old stub also collapsed all four real exercises into one invented 30-question group with no solutions file behind it. Every matrix computation in this file (all 56 questions) was independently verified with a Python script using numpy for numeric matrices and sympy for the symbolic ones (F(x)F(y)=F(x+y), the A'A=I system, and the two symbolic quadratic-in-x miscellaneous questions), catching zero discrepancies against the hand-derived working.. Questions are referenced from the NCERT textbook for identification.
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