Finding Inverse Using Elementary Transformations

Q.

Which of the following would be the Inverse of the matrix A found using Elementary Row Transformations where

A =$\left|\begin{array}{ccc}1& 3& 1\\ 0& 1& 1\\ 3& 6& 1\end{array}\right|$

1. $\left[\begin{array}{ccc}-5& +3& 2\\ 3& -2& -1\\ 3& +3& 1\end{array}\right]$

2. $\left[\begin{array}{ccc}-5& +3& 2\\ 3& 2& -1\\ -3& +3& 1\end{array}\right]$

3. $\left[\begin{array}{ccc}-5& +3& 2\\ 3& -2& -1\\ -3& +3& 1\end{array}\right]$

4. $\left[\begin{array}{ccc}-5& +3& 2\\ 3& 2& -1\\ -3& +3& 1\end{array}\right]$

Q. Let $A=\left[a_{ij}\right]$ is a $5\times 5$ upper triangular matrix, then which of the following statement(s) is(are) correct

1. Minimum number of zeros in $A$ are $15.$
2. Maximum number of zeros in $A$ are $25.$
3. Maximum number of zeros in $A$ are $24.$
4. Minimum number of zeros in $A$ are $10.$

Q. The value of $\left|\begin{array}{ccc}{a}^2+1& ab& ac\\ ab& b^2+1& bc\\ ac& bc& c^2+1\end{array}\right|$ is:

1. $1+a+b+c$
2. $1+a^3+b^3+c^3$
3. $abc$
4. $1+a^2+b^2+c^2$