Match List-I with List-II | List-I | List-II | | --- | --- | | (A) If $A$ is a non-singular matrix of order $n$, then $\vert A(\text{adj} A)\vert $ is equal to | (I) $\vert A\vert ^{n-1}$ | | (B) If $A$ is a non-singular matrix of order $n$, then $\vert \text{adj}(\text{adj} A)\vert $ is equal to | (II) $\vert A\vert ^{n-2} A$ | | (C) If $A$ is a non-singular matrix of order $n$, then $\text{adj}(\text{adj} A)$ is equal to | (III) $\vert A\vert ^n$ | | (D) If $A$ is a non-singular matrix of order $n$, then $\vert (\text{adj} A)\vert $ is equal to | (IV) $\vert A\vert ^{(n-1)^2}$ | Choose the correct answer from the options given below:

Let A, B, C be square matrices of equal orders and I be the identity matrix of same order, Then which of the following are TRUE?

A. $(AB)C = A(BC)$

B. $AB = BA$

C. $A(B+C) = AB + AC$

D. $AI = IA = A$

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$

If $A = \begin{bmatrix} 2 & -1 & 0 \\ 1 & 1 & 2 \\ -1 & 0 & 1 \end{bmatrix}$, then which of the following statement(s) is/are correct?

(A) A is singular matrix

(B) |3A| = 135

(C) |adj A| = 125

(D) $|A^{-1}| = \frac{1}{5}$

Choose the correct answer from the options given below:

If $P=\left[\begin{array}{r}-1 \\ 2 \\ 1\end{array}\right]$ and $Q=\left[\begin{array}{lll}2 & -4 & 1\end{array}\right]$ are two matrices, then $(P Q)^{\prime}$ will be :

If $\left[\begin{array}{cc}5 x+8 & 7 \\ y+3 & 10 x+12\end{array}\right]=\left[\begin{array}{cc}2 & 3 y+1 \\ 5 & 0\end{array}\right]$, then the value of $5 x+3 y$ is equal to :

The number of all possible matrices of order 3 x 3 with each entry belonging to the set {0, 1} is: