If $A = \begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$, then the value of $1000|A^n| + 2|A|$ for a positive integer $n$, is equal to

If $A = \begin{bmatrix} 5 & 6 \\ 3 & 2 \end{bmatrix}$ then which of the following is correct?

(A) $|A|$ is positive

(B) $|adj\ A| = -8$

(C) Cofactor of 3 is 6

(D) $|2A| = -32$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively:

Let P and Q be any two invertible matrices of the same order. Then

Match List-I with List-II

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The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then

Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: