If A and B are invertible matrices of the same order, then

Match List-I with List-II

List-I (Determinant)	List-II (Equal to)
(A) $\left\vert A^{-1}B \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert \left\vert B \right\vert}$
(B) $\left\vert AB^{-1} \right\vert$	(II) $\dfrac{\left\vert B \right\vert}{\left\vert A \right\vert}$
(C) $\left\vert A^{-1}B^{-1} \right\vert$	(III) $\left\vert A \right\vert \left\vert B \right\vert$
(D) $\left\vert AB \right\vert$	(IV) $\dfrac{\left\vert A \right\vert}{\left\vert B \right\vert}$

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If $A = \begin{bmatrix}\alpha & \beta\\r & \Delta\end{bmatrix}$, such that $|A| = 25$, then the value of $\left|\frac{1}{5}A\right|$ is.

Which of the following are correct?

(A) For a square matrix A, if A³ = I, then A⁻¹ = A².

(B) The determinant of only a square matrix can be defined.

(C) If A is a square matrix of order 3, then the number of minors of the matrix A is 3.

(D) If A and B are two non-singular matrices of the same order, then (AB)⁻¹ = B⁻¹A⁻¹.

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Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$.

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

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If $A = \begin{pmatrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \end{pmatrix}$, then $A^2 =$

If $\begin{bmatrix} x-2y & z \\ 3x+y & w \end{bmatrix}=\begin{bmatrix} 1 & 2 \\ -11 & 1 \end{bmatrix}$; then the value of $y-x$ is:-

If A is a square matrix of order 3, then |adj A| is equal to: