Matrices

Showing 1-5 of 203 questions.

Page 1 of 42

JEE Main 2021 (Online) 17th March Morning ShiftQuestion 1

If $A=\begin{pmatrix}0&\sin\alpha\\ \sin\alpha&0\end{pmatrix}$ and $\det\left(A^{2}-\frac{1}{2}I\right)=0$, then a possible value of $\alpha$ is :

Matrices

$\frac{\pi}{4}$$\frac{\pi}{3}$$\frac{\pi}{6}$$\frac{\pi}{2}$

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 2

Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A^{2}$ is $1$, then the possible number of such matrices is :

Matrices

$1$$4$$6$$12$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 3

Let $A=[a_{ij}]$ be a real matrix of order $3\times3$, such that $a_{i1}+a_{i2}+a_{i3}=1$, for $i=1,2,3$. Then, the sum of all the entries of the matrix $A^{3}$ is equal to :

Matrices

$1$$2$$3$$9$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 4

Let $A=\begin{bmatrix}\alpha&1&2\\2&3&0\\0&4&5\end{bmatrix}$ and $B=\begin{bmatrix}1&0&0\\0&-5\alpha&0\\0&4\alpha&-2\alpha\end{bmatrix}+\operatorname{adj}(A)$. If $\det(B)=66$, then $\det(\operatorname{adj}(A))$ equals :

Matrices

$289$$361$$441$$529$

JEE Main 2021 (Online) 18th March Morning ShiftQuestion 5

Let $A+2B=\begin{bmatrix}1&2&0\\6&-3&3\\-5&3&1\end{bmatrix}$ and $2A-B=\begin{bmatrix}2&-1&5\\2&-1&6\\0&1&2\end{bmatrix}$. If $\operatorname{Tr}(A)$ denotes the sum of all diagonal elements of the matrix $A$, then $\operatorname{Tr}(A)-\operatorname{Tr}(B)$ has value equal to :

Matrices

$1$$2$$3$$0$