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Matrices

CBSE Class 12 · Mathematics · 34 past questions

  1. Q1 2026
    Which of the following cannot be the order of a row-matrix ?
  2. Q2 2026
    If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew…
  3. Q3 2026
    If A and B are square matrices of same order, then which of the following statements is/are always true ?…
  4. Q4 2026
    If $A = \begin{bmatrix} 1 & a & b \\ -1 & 2 & c \\ 0 & 5 & 3 \end{bmatrix}$ is a symmetric matrix, then the…
  5. Q5 2026
    If A = $\begin{bmatrix}\cos x & -\sin x\\ \sin x & \cos x\end{bmatrix}$ and A + A' = I, then the value of…
  6. Q6 2026
    If A and B are skew-symmetric matrices of same order, then $AB' + BA'$ is a/an…
  7. Q7 2026
    If $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$, then order of A…
  8. Q8 2026
    If a square matrix A is such that $A^2 = A$ and $(I - A)^3 = xA + I$, then value of x must be…
  9. Q9 2025
    Let $A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}$…
  10. Q10 2025
    If $A = \begin{bmatrix} 7 & 0 & x \\ 0 & 7 & 0 \\ 0 & 0 & y \end{bmatrix}$ is a scalar matrix, then $y^x$ is…
  11. Q11 2025
    If A and B are invertible matrices, then which of the following is not correct ?
  12. Q12 2025
    If $A = \begin{bmatrix} 1 & 12 & 4y \\ 6x & 5 & 2x \\ 8x & 4 & 6 \end{bmatrix}$ is a symmetric matrix, then…
  13. Q13 2025
    Which of the following can be both a symmetric and skew-symmetric matrix ?
  14. Q14 2025
    Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB + 3(AB + BA) – 4 BA, where A and B…
  15. Q15 2025
    If A and B are square matrices of order m such that $A^2 - B^2 = (A - B)(A + B)$, then which of the following…
  16. Q16 2025
    If A and B are square matrices of same order such that AB = A and BA = B, then $A^2 + B^2$ is equal to…
  17. Q17 2025
    The matrix $\begin{bmatrix}0&1&-2\\-1&0&-7\\2&7&0\end{bmatrix}$ is a…
  18. Q18 2024
    If a matrix has 36 elements, the number of possible orders it can have, is…
  19. Q19 2024
    If $\begin{bmatrix} x+y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}$, then the…
  20. Q20 2024
    If A and B are two non-zero square matrices of same order such that $(A + B)^2 = A^2 + B^2$, then…
  21. Q21 2024
    $If A = [a_{ij}] is an identity matrix, then which of the following is true ?$
  22. Q22 2024
    If A and B are two skew symmetric matrices, then $(AB + BA)$ is…
  23. Q23 2024
    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
  24. Q24 2024
    If the sum of all the elements of a $3 \times 3$ scalar matrix is 9, then the product of all its elements is…
  25. Q25 2024
    If $A = [a_{ij}]$ be a $3 \times 3$ matrix, where $a_{ij} = i - 3j$, then which of the following is *false* ?
  26. Q26 2024
    If $F(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and…
  27. Q27 2024
    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
  28. Q28 2023
    If $A = \begin{bmatrix} 1 & 4 & x \\ z & 2 & y \\ -3 & -1 & 3 \end{bmatrix}$ is a symmetric matrix, then the…
  29. Q29 2023
    A and B are skew-symmetric matrices of same order. AB is symmetric, if…
  30. Q30 2023
    For what value of $x \in \left[0, \dfrac{\pi}{2}\right]$, is $A + A' = \sqrt{3}\, I$, where…
  31. Q31 2023
    If $A = \begin{bmatrix} 3 & 4 \\ 5 & 2 \end{bmatrix}$ and $2A + B$ is a null matrix, then $B$ is equal to…
  32. Q32 2023
    If $A = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$ and $(3I + 4A)(3I - 4A) = x^2 I$, then the value(s)…
  33. Q33 2023
    If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$, then $A^{2023}$ is equal to
  34. Q34 2023
    If $\begin{bmatrix} 2 & 0 \\ 5 & 4 \end{bmatrix} = P + Q$, where P is a symmetric and Q is a skew symmetric…