If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, then $A^2 - 5A + 7I =$

If $\begin{vmatrix} -1 & a & a^2 \\ -1 & b & b^2 \\ -1 & c & c^2 \end{vmatrix}^2 = \lambda$ and $a - b = 1$, $b - c = 2$ and $c - a = 3$, then the value of $\lambda$ is

Let $A = [a_{ij}]_{3\times3}$ be a matrix such that $a_{ij} = \dfrac{i-j}{i+j}$, then which of the following statements is/are TRUE?

A. A is a symmetric matrix

B. A is a skew symmetric matrix

C. $|A| = 0$

D. $|A| \neq 0$

Choose the correct answer from the options given below:

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

If the points (a, b), (c, d) and (a + c, b + d) are collinear, then

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of $A^2 - 5A + 6I$ is

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 \\ 3 & -4 \\ 2 & 4 \end{bmatrix}$, then $AB$ is :