Embibe Experts Solutions for Chapter: Matrices & Determinants, Exercise 2: Exercise 2

If $M\left(\alpha \right)=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0\\ \sin \alpha & \cos \alpha & 0\\ 0& 0& 1\end{array}\right],$ $M\left(\beta \right)=\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]$, then ${\left[M\left(\alpha \right)M\left(\beta \right)\right]}^{-1}$ is equal to

If $A=\left[\begin{array}{ll}1& 2\\ 3& 0\end{array}\right], B=\left[\begin{array}{ll}3& 4\\ 1& 6\end{array}\right]$ then, which of the following statements is true.

If $A=\left[\begin{array}{ccc}1& -5& 7\\ 0& 7& 9\\ 11& 8& 9\end{array}\right],$ then trace of matrix $A$ is

If $E\left(\theta \right)=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right],$ then the value of $E\left(\alpha \right)·E\left(\beta \right)$ is

If $A=\left[\begin{array}{cc}-1& 7\\ 2& 3\end{array}\right],$ then skew-symmetric part of $A$ is

If $A, B$ and $C$ are the angles of a non-right angled triangle $ABC$, then the value of $\left|\begin{array}{ccc}\tan A& 1& 1\\ 1& \tan B& 1\\ 1& 1& \tan C\end{array}\right|$ is equal to

The value of the determinant $\left|\begin{array}{ccc}1& \cos \left(\alpha -\beta \right)& \cos \alpha \\ \cos \left(\alpha -\beta \right)& 1& \cos \beta \\ \cos \alpha & \cos \beta & 1\end{array}\right|$ is

If $A=\left[\begin{array}{ccc}0& -1& 2\\ 2& -2& 0\end{array}\right], B=\left[\begin{array}{cc}0& 1\\ 1& 0\\ 1& 1\end{array}\right]$ and $M=AB,$ then $M^{-1}$ is equal to