Determinants Te...

$$A = \begin{bmatrix}1&2\\3&4\end{bmatrix}, B = \begin{bmatrix}2&1\\3&4\end{bmatrix}$$ then $$\left|(B^TA^T)^{-1}\right|$$ is equal to

If $$\begin{vmatrix}a&a^3 &a^4-1\\b&b^3&b^4-1\\c&c^3&c^4-1\end{vmatrix}=0$$ and $$a,b,c$$ are all distinct then $$abc (ab+bc+ca)$$ is equal to

If three points $$(k, 2k), (2k, 3k), (3, 1)$$ are collinear, then $$k$$ is equal to:

$$\left|\begin{array}{lllll}
0 & & \mathrm{c}\mathrm{o}\mathrm{s}\alpha & \mathrm{c}\mathrm{o}\mathrm{s} & \beta\\
\mathrm{c}\mathrm{o}\mathrm{s} & \alpha & 0 & \mathrm{c}\mathrm{o}\mathrm{s} & \gamma\\
\mathrm{c}\mathrm{o}\mathrm{s} & \beta & \mathrm{c}\mathrm{o}\mathrm{s}\gamma & 0 &
\end{array}\right|=$$

If A $$ =\begin{bmatrix}
0 & c &-b \\
-c& 0& a\\
b & -a & 0
\end{bmatrix}$$ then $$\left ( a^{2}+b^{2}-c^{2} \right )\left | A \right |=$$ 

$$\begin{vmatrix}
x^{2}+3 &x-1 &x+3 \\
x+3 & -2x &x-4 \\
x-3& x+4 & 3x
\end{vmatrix}$$ $$=px^{4}+qx^3+rx^{2}+sx+t,$$  then $$t = $$

Maximum value of a second order determinant whose every element is either 0,1 or 2 only is:

If abc $$\neq $$0 and if $$\begin{vmatrix}
a & b & c\\
b & c & a\\
c & a & b
\end{vmatrix}$$ = 0 then $$\dfrac{a^{3}+b^{3}+c^{3}}{abc}$$ 

If P =$$\begin{bmatrix}
1 & 4\\
2 & 6
\end{bmatrix}$$ ,then adj (P) 

If $$A=\left\{\begin{array}{lll}
a & b & c\\
b & c & a\\
c & a & b
\end{array}\right\}$$ then cofactor of $$\mathrm{a}_{21}$$ is: