Matrices And Determinants — JEE Advanced Previous Year Questions

How many JEE Advanced questions come from Matrices And Determinants?

Matrices And Determinants has contributed 34 questions to Joint Entrance Examination (Advanced) papers between 2016 and 2026 — an average of about 3 questions a year. That count is measured from EByAi’s bank of 18,502 JEE Advanced questions, not estimated from a syllabus. Every one of the 34 questions carries a written, step-by-step solution, and each is tagged to Matrices And Determinants 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 And Determinants questions from real JEE Advanced papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 34 Matrices And Determinants questions (with full written solutions) are available in practice.

1. Question 1 · JEE Advanced 2026

   Which one of the following matrices can be obtained by performing elementary row transformations on the $3\times 3$ identity matrix?
   1. (A)$$\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]$$
   2. (B)$$\left[\begin{array}{ccc}1& 1& 1\\ 2& 3& 4\\ 1& 2& 1\end{array}\right]$$
   3. (C)$$\left[\begin{array}{ccc}1& 1& 1\\ 2& 3& 4\\ 2& 5& 8\end{array}\right]$$
   4. (D)$$\left[\begin{array}{ccc}1& 1& 1\\ -1& 1& 2\\ 0& 2& 3\end{array}\right]$$
   Show answerAnswer

   Answer: (B) $$\left[\begin{array}{ccc}1& 1& 1\\ 2& 3& 4\\ 1& 2& 1\end{array}\right]$$

2. Question 2 · JEE Advanced 2025

   Consider the matrix $$P=\left(\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right).$$ Let the transpose of a matrix $X$ be denoted by $X^T$. Then the number of $3\times 3$ invertible matrices $Q$ with integer entries, such that $Q^{-1}=Q^T\text{and}PQ=QP,$ is
   1. (A)32
   2. (B)8
   3. (C)16
   4. (D)24
   Show answerAnswer

   Answer: (C) 16

3. Question 3 · JEE Advanced 2022

   If $$M=\left(\begin{array}{rr}\frac{5}{2}& \frac{3}{2}\\ -\frac{3}{2}& -\frac{1}{2}\end{array}\right)$$, then which of the following matrices is equal to $M^{2022}?$
   1. (A)$$\left(\begin{array}{rr}3034& 3033\\ -3033& -3032\end{array}\right)$$
   2. (B)$$\left(\begin{array}{ll}3034& -3033\\ 3033& -3032\end{array}\right)$$
   3. (C)$$\left(\begin{array}{rr}3033& 3032\\ -3032& -3031\end{array}\right)$$
   4. (D)$$\left(\begin{array}{rr}3032& 3031\\ -3031& -3030\end{array}\right)$$
   Show answerAnswer

   Answer: (A) $$\left(\begin{array}{rr}3034& 3033\\ -3033& -3032\end{array}\right)$$

4. Question 4 · JEE Advanced 2017

   $$Howmany3\times 3matricesMwithentriesfrom0,1,2arethere,forwhichthesumofthediagonalentriesof{M}^{T}Mis5?$$
   1. (A)198
   2. (B)162
   3. (C)126
   4. (D)135
   Show answerAnswer

   Answer: (A) 198

5. Question 5 · JEE Advanced 2016

   Let P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right] and I be the identity matrix of order 3. If $Q=[q_{ij}]$ is a matrix such that $P^{50}-Q=I$ and $\frac{q_{31}+q_{32}}{q_{21}}$ equals
   1. (A)52
   2. (B)103
   3. (C)201
   4. (D)205
   Show answerAnswer

   Answer: (B) 103

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