Find out the unit matrix of order $4\times 4$.

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 $\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$

$A={\left[a_{ij}\right]}_{m\times n}$ is a square matrix, if 

If $A=\left[\begin{array}{rrr}-1& 1& 2\\ 3& 0& 4\\ 2& 1& -2\end{array}\right]$ and $B=\left[\begin{array}{rrr}2& -3& -4\\ -1& 0& -1\\ 0& -1& 0\end{array}\right]$, then examine whether the matrix $A^2-2B$ is singular.

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