Contact us
Back

Report Issue

Matrices

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN
Let A be a square matrix such that $A A^T=I$. Then $\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$ is equal to
JEE Main Mathematics Medium
View Solution →
Q JEE MAIN
Let $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ and $|2 A|^3=2^{21}$ where $...
JEE Main Mathematics Easy
View Solution →
Q JEE-Main 2024
If $\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}$ and $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$, then $\operatorname{det} \mathrm{X}$ is equal...
JEE Main Mathematics Easy
View Solution →
Q JEE MAIN 2024
Let $A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]$, where $B_1, \mathrm{~B}_2, \mathrm{~B}_3$...
JEE Main Mathematics Hard
View Solution →
Q JEE MAIN 2025
Let $\alpha, \beta(\alpha \neq \beta)$ be the values of $m$, for which the equations $x+y+z=1 ; x+2 y+4 z=m$ and $x+4 y+10 z=m^{2}$ have infinitely...
JEE Main Mathematics Easy
View Solution →
Q JEE MAIN 2025
Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 0 & 1\end{array}\right]$ and $\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \sin \theta & \cos \theta\end{array}\right], \theta>0$. If $\mathrm{B}=\mathrm{PAP}^{\mathrm{T}}, \mathrm{C}=\mathrm{P}^{\mathrm{T}} \mathrm{B}^{10} \mathrm{P}$ and...
JEE Main Mathematics Medium
View Solution →
Q JEE MAIN 2025
The number of singular matrices of order 2, whose elements are from the set {2,3,6,9}, is ______.
JEE Main Mathematics Hard
View Solution →
Q JEE MAIN 2025
Let A be a $3 \times 3$ matrix such that $|{\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} {\rm{A}}))| = 81$.
If $...
JEE Main Mathematics Medium
View Solution →
Q JEE MAIN 2025
Let $A = \left[ {\begin{array}{*{20}{c}} {\cos \theta }&0&{ - \sin \theta }\\ 0&1&0\\ {\sin \theta }&0&{\cos \theta } \end{array}} \right]$. If for some $...
JEE Main Physics Hard
View Solution →
Q JEE MAIN 2025
Let A be a matrix of order $3 \times 3$ and $|A| = 5$. If $...
JEE Main Mathematics Easy
View Solution →