Determinants Te...

Find the determinants of minors and cofactors of the determinant $$\begin{vmatrix}2 & 3 & 4\\ 7 & 2 & -5\\ 8 & -1 & 3\end{vmatrix}$$

Find the adjoint of the matrix $$A = \begin{bmatrix}1 & 2 & 3 \\ 1 & 3 & 5 \\ 1 & 5 & 12\end{bmatrix}$$.
If $$\mbox{Adjoint A: } \begin{bmatrix}a & -9 & 1 \\ b & 9 & -2 \\ 2 & c & 1\end{bmatrix} \\$$, find the value of $$abc$$.

If $$A^2 = I$$, then the value of $$det(A - I)$$ is (where $$A$$ has order $$3$$)

If $$A=\begin{vmatrix} 1 & 2 \\ 2 & 1 \end{vmatrix}$$and $$f(x) = \displaystyle \frac{1 + x}{1- x}$$, then $$f(|A|)$$ is

$$\Delta =\begin{vmatrix} a & { a }^{ 2 } & 0 \\ 1 & 2a+b & (a+b) \\ 0 & 1 & 2a+3b \end{vmatrix}$$ is divisible by

If matrix A is given by $$A = \begin{bmatrix}6 & 11\\ 2 & 4\end{bmatrix}$$, then the determinant of $$A^{2005} - 6A^{2004}$$ is

$$\displaystyle \left | \begin{matrix}0 &p-q  &p-r \\ q-p &0  &q-r \\ r-p &r-q  &0 \end{matrix} \right |$$ is equal to

If $$\displaystyle \left | \begin{matrix}6i &-3i  &1 \\ 4 &3i  &-1 \\ 20 &3  &i \end{matrix} \right |=x+iy$$ then

The matrix $$\begin{bmatrix}1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 1 & 1 \end{bmatrix}$$ is

The value of the determinant $$\displaystyle \left | \begin{matrix}^{5}C_{0} &^{5}C_{3}  &14 \\ ^{5}C_{1} &^{5}C_{4}  &1 \\ ^{5}C_{2} &^{5}C_{5}  &1 \end{matrix} \right |$$ is