Question 1 :
If $A = \begin{bmatrix} 1& \log_{b}a\\ \log_{a}b & 1\end{bmatrix}$ then $|A|$ is equal to<br>
Question 2 :
Let a be the square matrix of order 2 such that $A^2 - 4A + 4I =0$ where I is an identify matrix of order 2. .If$ B = A ^5 - 4A^4 + 6 A^3 + 4A^2 + A $ then Det (B) is equal to
Question 3 :
If the value of the determinant $\begin{vmatrix}m & 2\\ -5 & 7\end{vmatrix}$ is $31$, find $m$.
Question 4 :
If $\omega$ is a cube root of unity and $\Delta=\begin{vmatrix}1 & 2\omega \\ \omega & \omega^2\end{vmatrix}$, then $\Delta^2$ is equal to<br>
Question 5 : <div>Find x if it is given that:</div>$\det \left[\begin{array}{lll}<br/>2 & 0 & 0\\<br/>4 & 3 & 0\\<br/>4 & 6 & x<br/>\end{array}\right]=42$<br/>
Question 6 :
If A $ =\begin{bmatrix}<br>0 & c &-b \\ <br> -c& 0& a\\ <br>b & -a & 0<br>\end{bmatrix}$ then $\left ( a^{2}+b^{2}-c^{2} \right )\left | A \right |=$
Question 7 :
The value of the determinant $\begin{vmatrix}a & b & 0\\ 0 & a & b\\ b & 0 &a \end{vmatrix}$ is equal to
Question 8 :
If $A$ is a $3\times 3$ matrix and $\text{det} (3A)=k(\text{det} A)$, then $k=$
Question 9 :
If $A=\begin{bmatrix} a & b \\ b & a \end{bmatrix}$, then $\left| A+{ A }^{ T } \right| $ equals
Question 10 :
If $\begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy$, then<br>
Question 11 :
$\begin{vmatrix}<br>x^{2}+3 &x-1 &x+3 \\ <br>x+3 & -2x &x-4 \\ <br> x-3& x+4 & 3x<br>\end{vmatrix}$ $=px^{4}+qx^3+rx^{2}+sx+t,$ then $t = $
Question 12 :
$D\mathrm{e}\mathrm{t} \left\{\begin{array}{lll}<br>2 & 45 & 55\\<br>1 & 29 & 32\\<br>3 & 68 & 87<br>\end{array}\right\}=\ldots.$ .<br>
Question 13 :
The value of the determinant $\begin{vmatrix} 1 & 2 & 3\\ 3 & 5 & 7\\ 8 & 14 & 20\end{vmatrix}$ is equal to<br>
Question 14 :
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 15 : <div><div><span>Two $n\times n$ square matrices A and B are said to be similar if there exists a non-singular matrix P such that </span><span>$P^{-1}A  P=B$.</span><br/></div></div>If A and B are similar matrices such that $det  (A)=1$, then
Question 16 :
$\left|\begin{array}{lllll}<br>0 & & \mathrm{c}\mathrm{o}\mathrm{s}\alpha & \mathrm{c}\mathrm{o}\mathrm{s} & \beta\\<br>\mathrm{c}\mathrm{o}\mathrm{s} & \alpha & 0 & \mathrm{c}\mathrm{o}\mathrm{s} & \gamma\\<br>\mathrm{c}\mathrm{o}\mathrm{s} & \beta & \mathrm{c}\mathrm{o}\mathrm{s}\gamma & 0 & <br>\end{array}\right|=$<br>
Question 18 :
Maximum value of a second order determinant whose every element is either 0,1 or 2 only is:
Question 19 :
If $\begin{vmatrix}<br/>cos(A+B) & -sin(A+B) &cos2B \\ <br/> sin A& cos A &sin B \\ <br/> -cos A& sin A & cos B<br/>\end{vmatrix}$ =0 then B=<br/><br/><br/>
Question 21 :
Let a, b, c be three complex numbers, and let<br>$z=\begin{vmatrix}<br>0 & -b & -c\\ <br>b & 0 & -a\\ <br>c & a & 0<br>\end{vmatrix}$<br>then z equal<br>
Question 22 :
If $A$ is a skew symmetric matrix, then $\left| A \right| $ is
Question 23 :
If $\begin{vmatrix} x & y\\ 4 & 2 \end{vmatrix}=7$ and $\begin{vmatrix} 2 & 3\\ y & x \end{vmatrix}=4$ then<br>
Question 24 :
If $\begin{vmatrix}a & -b & -c\\-a & b & -c \\ -a & -b & -c\end{vmatrix}+\lambda abc=0$, then $\lambda$ is equal to<br>
Question 25 :
If $A$ is any skew-symmetric matrix of odd order then $\left| A \right| $ equals
Question 26 :
What is the value of the determinant<br>$\begin{vmatrix} 1!& 2! & 3!\\ 2! & 3! & 4! \\ 3!& 4!& 5!\end{vmatrix}$ <br> $?$
Question 27 :
If $a, b, c$ are non-zero and different from $1$, then the value of $\begin{vmatrix}\log_a 1 & \log_a b & \log_ac\\ \log_a \left( \dfrac{1}{b} \right ) & \log_b 1 &\log_a \left( \dfrac{1}{c} \right ) \\ \log_a \left( \dfrac{1}{c}\right ) & \log_a c & \log_c 1\end{vmatrix}$ is<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 :
If $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix}=\begin{vmatrix} 6 & 2 \\ 3x & 6 \end{vmatrix}$, then $x$ is equal to
Question 30 :
$\mathrm{If}$ $\left|\begin{array}{lll}<br>1 & 0 & 0\\<br>2 & 3 & 4\\<br>5 & -6 & x<br>\end{array}\right|$ $= 45$ $\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}$ $\mathrm{x}=$<br><br>
Question 31 :
If$\displaystyle \left | \begin{matrix}-12 &0   &\lambda  \\  0&  2& -1\\  2& 1 &15 \end{matrix} \right |=-360$, then the value of $\lambda$,is
Question 32 :
<i></i>What is the determinant of the matrix $\left [\begin{matrix} 3& 6\\ -1 & 2\end {matrix} \right]$?<br/>
Question 33 :
$\displaystyle \begin{vmatrix}cos\: C &tan\: A &0 \\ sin\: B &0 &-tan\: A \\ 0 &sin\: B &cos\: C \end{vmatrix}$ has the value<br>
Question 34 :
$\begin{vmatrix} 2^3 & 3^3 & 3.2^2+3.2+1\\ 3^3 & 4^3 & 3.3^2+3.3+1\\ 4^3 & 5^3 & 3.4^2+3.4+1\end{vmatrix}$ is equal to?
Question 35 :
If $x, y, z$ are positive numbers, then value of the determinant $\begin{vmatrix}1 & log_xy & log_xz \\ log_yx & 1 & log_yz\\ log_zx & log_zy & 1\end{vmatrix}$ is equal to<br/>
Question 36 :
If the determinant $\Delta =\begin{vmatrix} 3 & -2 & \sin { 3\theta } \\ -7 & 8 & \cos { 2\theta } \\ -11 & 14 & 2 \end{vmatrix}=0$, then the value of $\sin { \theta } $ is
