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

If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$4$
B.	$\vert A - I \vert$, I is identity matrix	II.	$-7$
C.	minor of $a_{32}$	III.	$0$
D.	cofactor $a_{32}$	IV.	$-4$

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For what values of $x$ and $y$, are the following matrices equal?

$A=\begin{bmatrix}2x+1 & 3y\\ 0 & y^2-5y\end{bmatrix}$, $B=\begin{bmatrix}x+3 & y^2+2\\ 0 & -6\end{bmatrix}$

If $A=[a_{ij}]_{3\times3}$ and $a_{ij}=2i-j$, then

Match List-I with List-II

List-I	List-II
(A) $a_{21}+a_{32}$	(I) 0
(B) $\lvert A\rvert$	(II) 19
(C) Number of the elements in A	(III) 7
(D) $a_{22}.a_{31}+a_{21}.a_{33}$	(IV) 9

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Which of the following are correct?

(A) If $A=\begin{bmatrix}7 & 5 \\ 4 & 3\end{bmatrix}$, then $A^{-1}=\begin{bmatrix}3 & -5 \\ -4 & 7\end{bmatrix}$

(B) If $A=\begin{bmatrix}3 & 5 \\ 6 & 10\end{bmatrix}$, then $A$ is a non-singular matrix

(C) $A=\begin{bmatrix}0 & -5 \\ 5 & 3\end{bmatrix}$ is a symmetric matrix

(D) If $A=\begin{bmatrix}6 & x \\ y & 0\end{bmatrix}$ and $A=A^T$, then $x=y$

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If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct?

(A) $|A| = 7$

(B) minor of $3 = -5$

(C) co-factor of $2 = -4$

(D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$

Choose the correct answer from the options given below:

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(C) Minimum value of $\Delta$ is $2$

(D) Maximum value of $\Delta$ is $4$

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