Find the maximum value of $\begin{vmatrix}1 & 1 & 1 \\ 1 & 1+sinθ & 1 \\ 1 & 1 & 1+cosθ\end{vmatrix}$

If x ∈ N and $\begin{vmatrix}x+3 & -2 \\ -3x & 2x\end{vmatrix}$ = 8, then find the value of x.

In the interval ${\frac{\pi}{2}}<x<\pi$ , find the value of x for which that matrix $\left(\begin{array}{l l }2sinx & 3 \\ 1 & 2sinx\end{array}\right)$ is singular.

Write the value of the determinant $\begin{vmatrix}p & p+1 \\ p-1 & p\end{vmatrix}$

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ , write the value of x.

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

If A and B are invertible matrices of order 3, $|\mathbf{A}|=$ 2 and $|(\mathbf{AB})^{-1}|\,=\,-{\frac{1}{6}}.$ Find $|\mathbf{B}$.

If A = $\left(\begin{array}{l l }4 & 6 \\ 7 & 5\end{array}\right)$ , then what is the value of $\ A{\cdot}(a d j A)$ ?

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ where α and β are acute angles, then write the value of α + β .

Evaluate x if : $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$

Given A = $\left(\begin{array}{l l l }4 & 2 & 5 \\ 2 & 0 & 3 \\ -1 & 1 & 0\end{array}\right)$ , write the value of det. $(2A A^{-1}).$

If A is square matrix of order 3 such that $|a d j A|=$ 64, find $|A|.$

If $\begin{vmatrix} 2x & x+3 \\ 2(x+1) & x+1 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, write the value of x.

For what value of x, the given matrix A = $\left(\begin{array}{l l }3-2x & x+1 \\ 2 & 4\end{array}\right)$ is a singular matrix ?

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.