If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$, then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)

Let $A$ and $B$ be two symmetric matrices of same order, then

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Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$, $a_{ij}=i+j$, then

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If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

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If P and Q are non-singular square matrices of the same order, then $(PQ^{-1})^{-1}$ equals

If $A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}$ be such that $A^{-1} = KA$, then the value of K is:

If $\begin{vmatrix}3 & x\\ x & 1\end{vmatrix}=\begin{vmatrix}3 & 2\\ 4 & 1\end{vmatrix}$, then value of $x$ is/are

(A) $x=2$

(B) $x=-2$

(C) $x=2\sqrt2$

(D) $x=-2\sqrt2$

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