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

For the system of linear equations : $$ x-2 y=I, x-y+k z=-2, k y+4 z=6, k \in R, $$ consider the following statements: (A) The...

Let $A$ and $B$ be $3 \times 3$ real matrices such that $A$ is symmetric matrix and $B$ is skew-symmetric matrix. Then the system of...

Let $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and $...

Let

The total number of 3 × 3 matrices A having enteries from the set (0, 1, 2, 3) such that the sum of all the...

Let $A=\left[\begin{array}{cc}i & -i \\ -i & i\end{array}\right], i=\sqrt{-1}$ Then, the system of linear equation $A^8=\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}8 \\ 64\end{array}\right]$ has :

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...

If $A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ \tan \left(\frac{\theta}{2}\right) & 0\end{array}\right]$ and $\left(I_2+A\right)\left(I_2-A\right)^{-1}= \left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$, then $13\left(a^2+b^2\right)$ is equal to $\_\_\_\_$...

Let $A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right]$, where $x, y$ and $z$ are real...