Matrices

CBSE Class 12 · Mathematics · 34 past questions

23 of 34 · show all

1. Q1 2026

   Which of the following cannot be the order of a row-matrix ?

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2. Q3 2026

   If A and B are square matrices of same order, then which of the following statements is/are always true ?…

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3. Q4 2026

   If $A = \begin{bmatrix} 1 & a & b \\ -1 & 2 & c \\ 0 & 5 & 3 \end{bmatrix}$ is a symmetric matrix, then the…

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4. Q5 2026

   If A = $\begin{bmatrix}\cos x & -\sin x\\ \sin x & \cos x\end{bmatrix}$ and A + A' = I, then the value of…

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5. 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…

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6. Q9 2025

   Let $A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}$…

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7. 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…

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8. Q11 2025

   If A and B are invertible matrices, then which of the following is not correct ?

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9. Q13 2025

   Which of the following can be both a symmetric and skew-symmetric matrix ?

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10. Q14 2025

    Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB + 3(AB + BA) – 4 BA, where A and B…

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11. Q17 2025

    The matrix $\begin{bmatrix}0&1&-2\\-1&0&-7\\2&7&0\end{bmatrix}$ is a…

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12. Q18 2024

    If a matrix has 36 elements, the number of possible orders it can have, is…

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13. Q19 2024

    If $\begin{bmatrix} x+y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}$, then the…

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14. 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…

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15. Q21 2024

    $If A = [a_{ij}] is an identity matrix, then which of the following is true ?$

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16. Q22 2024

    If A and B are two skew symmetric matrices, then $(AB + BA)$ is…

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17. Q23 2024

    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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18. 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…

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19. Q28 2023

    If $A = \begin{bmatrix} 1 & 4 & x \\ z & 2 & y \\ -3 & -1 & 3 \end{bmatrix}$ is a symmetric matrix, then the…

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20. Q30 2023

    For what value of $x \in \left[0, \dfrac{\pi}{2}\right]$, is $A + A' = \sqrt{3}\, I$, where…

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21. Q31 2023

    If $A = \begin{bmatrix} 3 & 4 \\ 5 & 2 \end{bmatrix}$ and $2A + B$ is a null matrix, then $B$ is equal to…

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22. Q33 2023

    If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$, then $A^{2023}$ is equal to

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23. Q34 2023

    If $\begin{bmatrix} 2 & 0 \\ 5 & 4 \end{bmatrix} = P + Q$, where P is a symmetric and Q is a skew symmetric…

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