If $\begin{vmatrix} (a-x)^2 & (a-y)^2 & (a-z)^2 \\ (b-x)^2 & (b-y)^2 & (b-z)^2 \\ (c-x)^2 & (c-y)^2 & (c-z)^2 \end{vmatrix} = \lambda(a-b)(b-c)(c-a) \cdot (x-y)(y-z)(z-x)$

then the value of $\lambda$ is:

If the system of equation

$\lambda x + 3y - z = 4$

$x + 2y + z = 20$

$-\lambda x + y + 2z = -5$

does not possess a unique solution, then

If A is a square matrix such that $A^2=A$ and $I$ is identity matrix of same order, then $(2I+A)^3-19A$ is equal to:

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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Let A = $[a_{ij}]_{n \times n}$ be a matrix. Then

Match List-I with List-II

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Match the LIST-I with LIST-II

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Let A, B, C, D and E be matrices of order $2 \times n, 3 \times k, 2\times p, n \times 3$ and $p \times k$ respectively. Choose the correct statement(s) from the following?

(A) EB + DB will be defined if $k = 3, p = n$.

(B) EB + DB will be defined if $k = 2, p = 3$.

(C) If n = p = 2, then the order of the matrix $5A^2 - 3C$ is $2 \times 2$.

(D) If n = p, then the order of the matrix $5A^2 - 3C$ is $p \times k$.

Choose the correct answer from the options given below: