The matrix $A=\left[\begin{array}{cc}\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\\ -\frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}\end{array}\right]$ is

Let $a, b, c\in R$ be all non-zero and satisfies $a^3+b^3+c^3=2$. If the matrix $A=\left[\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right]\begin{array}{}\\ \\ \end{array}$satisfies $A^{T}A=I,$ then a value of $abc$ can be

FInd the number of all possible matrices of order

$3\times 3$ with each entry $0$ or $1$.

Which of the given values of $x$ and $y$ make the following pair of matrices equal?

$\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]$ and $\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$