Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?

B is a null matrix if A is a non-singular matrix

Both A and B are singular matrices

Matrices — NDA Previous Year Questions

39 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 39
Years covered: 2021–2025
Avg / year: ~8
Subject: Mathematics

How many NDA questions come from Matrices?

Matrices has contributed 39 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 8 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 39 questions carries a written, step-by-step solution, and each is tagged to Matrices within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Matrices questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 39 Matrices questions (with full written solutions) are available in practice.

Question 1 · NDA 2024
Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?
1. (A) $Both A and B are null matrices$
2. (B) $Either A or B is a null matrix$
3. (C) $B is a null matrix if A is a non-singular matrix$
4. (D) $Both A and B are singular matrices$
Show answerAnswer
$Answer: (C) B is a null matrix if A is a non-singular matrix$
Question 2 · NDA 2023
The system of linear equations

x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has
1. (A) $a unique solution$
2. (B) $infinitely many solutions$
3. (C) $no solution$
4. (D) $exactly three solutions$
Show answerAnswer
$Answer: (C) no solution$
Question 3 · NDA 2023
Let AX = B be a system of 3 linear equations with 3 unknowns. Let X1 and X2 be its two distinct solutions. If the combination aX1 + bX2 is a solution of AX = B; where a, b are real numbers, then which one of the following is correct ?
1. (A) $a = b$
2. (B) $a + b = 1$
3. (C) $a + b = 0$
4. (D) $a - b = 1$
Show answerAnswer
$Answer: (B) a + b = 1$
Question 4 · NDA 2023
Consider the following statements in respect of square matrices A, B, C each of the same order n:
1. AB = AC ⇒ B = C if A is non-singular
1. If BX = CX for every column matrix X having n rows then B = C
Which of the statements given above is/are correct?
1. (A) $1 only$
2. (B) $2 only$
3. (C) $Both 1 and 2$
4. (D) $Neither 1 nor 2$
Show answerAnswer
$Answer: (C) Both 1 and 2$
Question 5 · NDA 2023
Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?
1. Its diagonal entries are equal but nonzero
1. The sum of its non-diagonal entries is zero
Select the correct answer using the code given below :
1. (A) $1 only$
2. (B) $2 only$
3. (C) $Both 1 and 2$
4. (D) $Neither 1 nor 2$
Show answerAnswer
$Answer: (B) 2 only$

Matrices questions by year

Year	Questions	Share of chapter questions
2025	6
2024	10
2023	6
2022	10
2021	7

Practise these 39 questions with solutions

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FAQs

How many NDA questions have been asked from Matrices?

EByAi's bank holds 39 real NDA questions from Matrices, asked between 2021 and 2025 — about 8 per year on average. Every count is measured from actual papers, not estimated.

Is Matrices important for NDA?

39 questions over 5 papers make Matrices a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Matrices PYQs online for free?

Yes. EByAi lets you solve NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

More NDA Mathematics chapters

All NDA Mathematics chapters →NDA overview →