Value(s) of $x$ for which, $\begin{vmatrix} x & 1 \\ 5 & x \end{vmatrix} = \begin{vmatrix} 8 & 2 \\ 2 & 1 \end{vmatrix}$ is:

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

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If $a_{ij}$ and $A_{ij}$ represents the elements and cofactors of the matrix $A = \begin{bmatrix}2 & 1 & 3\\3 & 2 & 1\\1 & 2 & 3\end{bmatrix}$, then which of the following statements are True?

(A) $|A| = 28$

(B) $A_{23} = -3$

(C) $a_{11}A_{12} = -16$

(D) $\frac{A_{21}}{A_{13}} = \frac{3}{4}$

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If A and B are invertible matrices then which of the following statement is NOT correct?

Which of the following are true about the properties of transpose of appropriate matrices?

A. $(A+B)^T = A^T + B^T$

B. $(A-B)^T = A^T - B^T$

C. $(AB)^T = A^TB^T$

D. $(kA)^T = k(A^T)$, where k is a scalar

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If A is a matrix of order $3 \times 3$ such that $|A| = 4$ and $|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}$; then the value of k is:

If $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, Then

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