Which of the following are TRUE?

(A) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{27}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

(B) The determinant of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is 29.

(C) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{29}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

(D) The adjoint of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

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Let A be any square matrix of order 3 and $B = \begin{bmatrix} 0 & -4 & 2 \\ 4 & 0 & 3 \\ -2 & -3 & 0 \end{bmatrix}$. Then the matrix $ABA^T$ is a

Let $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -6 \\ -2 & 4 \end{bmatrix}$

(A) $\det(A^T) = 1$

(B) $AB = I$, where $I$ is the identity matrix of order 2.

(C) $A^{-1} = \begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$

(D) adj $(B) = \begin{bmatrix} 4 & 2 \\ 6 & 4 \end{bmatrix}$

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Which of the following are correct?

(A) $A=\begin{bmatrix}-9 & 4 & -3\\-1 & 0 & 4\\2 & 2 & 0\end{bmatrix}$ ; $a_{22}+a_{32}=-9$ where $a_{ij}$ denotes the $(i,j)^{th}$ element of matrix A.

(B) $A=\begin{bmatrix}2 & -2\\-2 & 2\end{bmatrix}$; $A^2=pA$, then $p=4$

(C) $\begin{bmatrix}8 & 6\\6 & 16\end{bmatrix}$ is a symmetric matrix

(D) $\begin{bmatrix}0 & -5 & 3\\5 & 0 & -7\\-3 & 7 & 0\end{bmatrix}$ is a symmetric matrix

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If A is a matrix of order $m \times n$ and B is another matrix such that $A'B$ and $BA'$ are both defined, then the order of matrix B is

If $\begin{bmatrix} 2a + b & a - 2b \\ 5c - d & 4c + 3d \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ 11 & 24 \end{bmatrix}$, then the value of $a + 2b - 3c + 4d$ is equal to

If $A = \begin{bmatrix} 1 & 2 \\ 4 & -3 \end{bmatrix}$ and $f(x) = 2x^2 - 4x + 5$, the $f(A)$ is equal to