R D Sharma Solutions for Chapter: Algebra of Matrices, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

If $A=\left[\begin{array}{cc}\cos x& \sin x\\ -\sin x& \cos x\end{array}\right]$, find $x$ satisfying $0 <x<\frac{\pi }{2}$ when $A+A^T=I$.

Find the value of $x$ from the following: $\left[\begin{array}{cc}2x-y& 5\\ 3& y\end{array}\right]=\left[\begin{array}{rr}6& 5\\ 3& -2\end{array}\right]$.

Find the value of $y$, if $\left[\begin{array}{ll}x-y& 2\\ x& 5\end{array}\right]=\left[\begin{array}{ll}2& 2\\ 3& 5\end{array}\right]$.

If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]$ is identity matrix, then the value of $\alpha =k°$, find the value of $k$.

If $I$ is the identity matrix and $A$ is a square matrix such that $A^2=A$, then what is the value of $(I+A{)}^2-3A$?

If $A$ is $2\times 3$ matrix and $B$ is a matrix such that $A^{T}B$ and $B{A}^T$ both are defined and order of $B$ is $m\times n$, then $m+n$ is

What is the total number of $2\times 2$ matrices with each entry $0$ or $1$?

For a $2\times 2$ matrix $A= \left[a_{ij}\right]$ whose elements are given by $a_{ij}=\frac{i}{j}$, write the value of $a_{12}$.