If A is a 3x3 matrix then:

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj A\vert$	I.	$\vert A\vert^{-1}$
B.	$\vert A.adj A\vert$	II.	$\vert A\vert$
C.	$\vert A^{-1}\vert$	III.	$\vert A\vert^2$
D.	$\vert A^{-1}.adj A\vert$	IV.	$\vert A\vert^3$

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Which of the following statement is/are correct?

(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i, j$

(D) The multiplication of diagonal matrices of same order is commutative

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If the matrix $\begin{bmatrix}3 & 2a & -5\\4 & 0 & b\\-5 & 3 & 10\end{bmatrix}$ is symmetric, then the value of $5a + 2b$ is

If A is a square matrix of order 4 and $|adj\,A| = 8$, then $|A| =$

Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$

(D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$

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If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$, then $|AA^T|$ is equal to:

If A and B are square matrices of the same order, then (A+B) (A-B) is equal to