Determinants — Important Questions
ICSE · Class 12 · Mathematics
100 important questions from Determinants for ICSE Class 12 Mathematics, with answers. Includes multiple choice and true false questions.
Interactive on Super Tutor
Studying Determinants? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for important questions and more.
Free trial, no card needed.
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Determinants.
Important Questions from Determinants
Every rectangular matrix has a determinant.
Show answer
False
Determinants are defined only for square matrices. Rectangular matrices (m×n with m≠n) do not have determinants.
For matrices A and B of the same order, |AB| equals:
Show answer
|A| × |B|
The product rule for determinants: |AB| = |A|·|B|. This is a fundamental property of determinants.
The value of |A| = |Aᵀ| for any square matrix A.
Show answer
True
Transposing a matrix does not change its determinant: |Aᵀ| = |A|. This is because determinant expansion by rows equals expansion by columns.
For a non-singular matrix A, A⁻¹ equals:
Show answer
(adj A)/|A|
A⁻¹ = (1/|A|) × adj A = (adj A)/|A|. This requires |A| ≠ 0 (non-singular).
+96 more questions on Determinants (ICSE Class 12 Mathematics)
Practise AllFrequently Asked Questions
What are the important topics in Determinants for ICSE Class 12 Mathematics?
How many important questions are there in Determinants?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Determinants
Practice Quiz
Test yourself with a quick quiz
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
For serious students
Get the full Determinants chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.