For any non-zero matrix $A = [a_{ij}]_{3\times3}$ and $|A| \neq 0$, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj\,A \vert$	I.	$\dfrac{1}{\vert A \vert}(adj\,A)$
B.	$(adj\,A)A$	II.	$\vert A \vert^2$
C.	$A^{-1}$	III.	$\dfrac{1}{\vert A \vert}$
D.	$\vert A^{-1} \vert$	IV.	$\vert A \vert I$

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If A (a, a − b), B (a + b, − b) and C (b, a) are three collinear points, where a, b, c, $\in \mathbb{R}$, then :

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 P and Q are symmetric matrices of same order, then $(PQ - QP)$ is

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$, then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

If A is an invertible matrix of order 3 and the determinant of A is 9, then the determinant of $A^{-1}$ is:

If A is an invertible matrix, then which of the following statement(s) is/are TRUE?

(A) $|A^{-1}| = |A|$

(B) $(A^{-1})^{-1} = A$

(C) $A^{-1} = \frac{adj A}{|A|}$

(D) $(A^T)^{-1} = (A^{-1})^T$

Choose the correct answer from the options given below: