If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

If $A = \begin{bmatrix} 3 & 2a \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ b & 5 \end{bmatrix}$ both are singular matrices, then $a + b$ is equal to

Which of the following statements is NOT CORRECT.

Choose the correct statement

A. If any two rows or any two columns are identical or proportional, then value of determinant is Zero.

B. Minor of an element $a_{ij}$ of the determinant of matrix A is the determinant obtained by deleting $i^{th}$ row and $j^{th}$ column

C. If $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$, then A is Skew-symmetric matrix

D. If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then $(A + A')$ is Symmetric matrix

E. If $|A| = 0$, then A is non-singular matrix

If $A=\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ such that $A^2-A+\lambda I=0$, then value of '$\lambda$' is:

If $\begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}P\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ then matrix P is

Let $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2 \end{bmatrix}$. $M_{ij}$ and $A_{ij}$ respectively denote the minor and cofactor of an element $a_{ij}$ of matrix $A = [a_{ij}]$

(A) $M_{23} = 6$

(B) $A_{22} = -8$

(C) $A_{13} = 7$

(D) $M_{32} = -5$

Choose the correct answer from the options given below: