Question 1 :
The number of different possible orders of matrices having 18 identical elements is
Question 2 :
What is the order of the product $$ \begin{bmatrix} x &  y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$$ ?
Question 3 :
If the sum of the matrices $$\begin{bmatrix} x \\ x \\ y \end{bmatrix},\begin{bmatrix} y \\ y \\ z \end{bmatrix}$$ and $$\begin{bmatrix} z \\ 0 \\ 0 \end{bmatrix}$$ is the matrix $$\begin{bmatrix} 10 \\ 5 \\ 5 \end{bmatrix}$$, then what is the value of $$y$$?
Question 4 :
The matrix $$A = \begin{bmatrix}0& 0 &4 \\ 0& 4 & 0\\ 4& 0 & 0\end{bmatrix}$$ is a<br>
Question 5 :
The entries of a matrix are integers. Adding an integer to all entries on a row or on a column is called an operation. It is given that for infinitely many integers N one can obtain, after a finite number of operations, a table with all entries divisible by N. Prove that one can obtain, after a finite number of operations, the zero matrix.
Question 6 :
The number of possible orders of a matrix containing $$24$$ elements are:
Question 7 :
Let  $$A$$  be a matrix such that  $$A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$$  is a scalar matrix and  $$| 3 A | = 108 .$$  Then    $$A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$$is equal to
Question 8 :
If $$ A= \begin{bmatrix} 1 & 2\end{bmatrix}, B=\begin{bmatrix} 3 & 4\end{bmatrix}$$ then $$A+B=$$
Question 9 :
If $$A= \begin{bmatrix} 1 & 2 & 3\end{bmatrix}$$, then order is
Question 10 :
The order of $$\begin{bmatrix}x & y & z\end{bmatrix}\begin{bmatrix}a & h & g \\ h & b & f \\ g & f & c\end{bmatrix}\begin{bmatrix}x\\ y \\z\end{bmatrix}$$ is
Question 11 :
If P=$$\displaystyle  \begin{bmatrix} 4 & 3 &2   \end{bmatrix}  $$ and Q=$$\displaystyle  \begin{bmatrix} -1 & 2 &3   \end{bmatrix}  $$ then P-Q=
Question 12 :
If $$\displaystyle A=\left [ a_{ij} \right ]_{m\times\:n'}B=\left [ b_{ij} \right ]_{m\times\:n'}$$ then the element $$\displaystyle C_{23}$$ of the matrix $$C=A+B$$, is:
Question 13 :
A matrix having $$m$$ rows and $$n$$ columns with $$m=n$$ is said to be a 
Question 14 :
IF A=$$\displaystyle \begin{vmatrix} 5 & x \\ y & 6 \end{vmatrix} $$ B=$$\displaystyle \begin{vmatrix} -4 & y \\ -4 & -5 \end{vmatrix} $$and A+B=I then the values of x and y respectively are
Question 15 :
If A=$$\displaystyle \begin{vmatrix} 0 & 1 \\ 2 & 4 \end{vmatrix} $$, B=$$\displaystyle \begin{vmatrix} -1 & 1 \\ 2 & 2 \end{vmatrix} $$,<br>C=$$\displaystyle \begin{vmatrix} 1 & 0 \\ 1 & 0 \end{vmatrix} $$, then 2A+3B-C=<br>
Question 16 :
Let $$\omega\neq{1}$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$ \begin{bmatrix} 1 & a & b \\ \omega & 1 & c \\ { \omega }^{ 2 } & \omega & 1 \end{bmatrix}$$Where each of $$a,\ b$$ and $$c$$ is either $$\omega$$ or $${\omega}^{2}$$. Then the number of distinct matrices in the set $$S$$ is
Question 17 :
$$\displaystyle \Delta = \begin{vmatrix}1 & \log_{x}y  & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log _{z}x  &\log _{z}y  & 1\end{vmatrix}$$ is equal to <br/> <br/>
Question 18 :
Find the value of $$x$$ in $$\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$$.
Question 19 :
If abc $$\neq $$0 and if $$\begin{vmatrix}<br/>a & b & c\\ <br/>b & c & a\\ <br/>c & a & b<br/>\end{vmatrix}$$ = 0 then $$\dfrac{a^{3}+b^{3}+c^{3}}{abc}$$ 
Question 20 :
Let the matrix A and B be defined as $$A =\begin{vmatrix} 3 & 2 \\ 2 & 1 \end{vmatrix}$$ and $$B =\begin{vmatrix} 3 & 1 \\ 7 & 3 \end{vmatrix}$$ then the value of Det.$$(2A^9B^{-1})$$, is
Question 21 :
Find the values of x, if <br>$$\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}$$= $$\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$$
Question 22 :
<i></i>What is the determinant of the matrix $$\left [\begin{matrix} 3& 6\\ -1 & 2\end {matrix} \right]$$?<br/>
Question 23 :
$$A=\begin{bmatrix} 5 & 5a & a \\ 0 & a & 5a \\ 0 & 0 & 5 \end{bmatrix}$$ If $$\left| A^{ 2 } \right| =25$$ then $$|a|=$$
Question 24 :
If $$\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$$ then $$x$$=
Question 25 :
If the trivial solution is the only solution of the system of equations$$x-ky+z=0,kx+3y-kz=0, 3x+y-z=0$$. Then the set of all values of k is:<br>
Question 26 :
$$\mathrm{If}$$ $$\left|\begin{array}{lll}<br>1 & 0 & 0\\<br>2 & 3 & 4\\<br>5 & -6 & x<br>\end{array}\right|$$ $$= 45$$ $$\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}$$ $$\mathrm{x}=$$<br><br>
Question 27 :
Find x if it is given that:$$\det \left[\begin{array}{lll}<br/>2 & 0 & 0\\<br/>4 & 3 & 0\\<br/>4 & 6 & x<br/>\end{array}\right]=42$$<br/>
Question 28 :
If $$\Delta_1=\begin{vmatrix} 1 & 0\\ a & b\end{vmatrix}$$ and $$\Delta_2=\begin{vmatrix} 1 & 0\\ c & d\end{vmatrix}$$ then $$\Delta_2 \Delta_1$$ is equal to<br>
Question 29 :
Find the value of the following determinant:<br/>$$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$$
Question 30 :
The determinant $$\begin{vmatrix}a & b & a\alpha +b\\ b & c & b\alpha +c\\ a\alpha +b & b\alpha +c & 0\end{vmatrix}$$ is equal to zero, if.
