D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Matrices & Determinants, Exercise 1: Exercise 1

If $I_n$ is the identity matrix of order $n$, then rank of $I_n$ is

If the points $\left(x_1,y_1\right)$, $\left(x_2,y_2\right)$ and $\left(x_3,y_3\right)$ are collinear, then the rank of the matrix $\left[\begin{array}{lll}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right]$ will always be less, than

If $A=\left[\begin{array}{lll}2& 0& 0\\ 2& 2& 0\\ 2& 2& 2\end{array}\right]$, then $\mathrm{adj}\left(\mathrm{adj}A\right)$ is equal to 

If $A=\left[\begin{array}{ll}3& 4\\ 5& 7\end{array}\right],$ then $A·\left(\mathrm{adj} A\right)$ is equal to

If $A=\left[\begin{array}{cc}p& q\\ -q& p\end{array}\right], B=\left[\begin{array}{cc}r& s\\ -s& r\end{array}\right]$, then

If $∆\left(x\right)=\left|\begin{array}{ccc}1& \cos x& 1-\cos x\\ 1+\sin x& \cos x& 1+\sin x-\cos x\\ \sin x& \sin x& 1\end{array}\right|$, then ${\int }_0^{\pi /4}∆\left(x\right)dx$ is equal to

If $\left[\begin{array}{cc}1& 0\\ 3& -4\end{array}\right]+\left[\begin{array}{cc}a& 1\\ -1& b\end{array}\right]=\left[\begin{array}{cc}2& 1\\ 2& -2\end{array}\right],$ then value of $a, b$ are

The digits $A, B$ and $C$ are such that the three digit numbers $A88, 6B8, 86C$ are divisible by $72$, then the determinant $\left|\begin{array}{lll}A& 6& 8\\ 8& B& 6\\ 8& 8& C\end{array}\right|$ is divisible by