List of top Mathematics Questions on Determinant

M is a square matrix of order 3. If \[ M(\operatorname{adj} M)= \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then the value of \[ |M+\operatorname{adj} M| \] is equal to: 

The determinant \( \begin{vmatrix} \lambda & \sin\theta & \cos\theta \\ -\sin\theta & -\lambda & 1 \cos\theta & 1 & \lambda \end{vmatrix} \) is equal to:
Value of the determinant \(\begin{vmatrix} \log_{3}512 & \log_{4}3 \\ \log_{3}8 & \log_{4}9 \end{vmatrix}\) is:
If \( A \) is a skew-symmetric matrix of order \( 5 \times 5 \), what is the value of its determinant \( |A| \)?
If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = 2abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]
If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]
If \( A \) is a square matrix of order \(3\) and \( |A|=-3 \), then the value of \( |2AA^T| \) is:
If \( A \) is a square matrix of order \(3\) such that \( |2(\operatorname{adj}A)|=288 \), then the value of \( |A| \) is:
Solve: \[ \begin{vmatrix} x & 1\\ 2 & x \end{vmatrix}=0 \]
Evaluate: \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \)
If \( A = \begin{bmatrix} -2 & 0 & 0 \\ 1 & 2 & 3 \\ 5 & 1 & -1 \end{bmatrix} \), then the value of \( |A \cdot \text{adj}(A)| \) is:

Given that $ A^{-1} = \frac{1}{7} \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix} $, matrix $ A $ is:

\( x \log x \frac{dy}{dx} + y = 2 \log x \) is an example of a:
If \[ \begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \] has a determinant of \( \pm 6 \), then the value of \( k \) is: