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 $\begin{vmatrix} 1+x^2 & 1 & 1 \\ 1 & 1+y^2 & 1 \\ 1 & 1 & 1+z^2 \end{vmatrix} = k\left(1 + \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$ then $k$ is equal to

Which of the following statements are correct ?

A. If the product of 2 non-zero square matrices is a zero matrix, then either A is singular or B is singular

B. If A is a non singular matrix , then $|A^{-1}| = \dfrac{1}{|A|}$

C. If A is an invertible square matrix then $adj\,A^T = \dfrac{1}{adj\,A}$

D. If A and B are invertible matrices then $(AB)^{-1} = B^{-1}A^{-1}$

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Let $A=\begin{bmatrix}1 & \sin\theta & 1\\-\sin\theta & 1 & \sin\theta\\-1 & -\sin\theta & 1\end{bmatrix}$, where $\theta\in[0,2\pi]$ then which of the following statements are correct?

A. $|A|=2+2\sin^2\theta$

B. Maximum value of $|A|$ is 1.

C. Maximum value of $|A|$ is –1.

D. $|A|\in[2,4]$

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Given that $Y_{3\times k}$, $W_{n\times 3}$ and $P_{p\times k}$ are matrices of specified order, then the condition for n, p, k so that $3PY + 2WY$ is well defined, is:

If $A$ and $B$ are symmetric matrices of the same order, then $A B-B A$ is a :

The matrix $\begin{bmatrix} 2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4 \end{bmatrix}$ is not invertible for