The matrix $\begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is a

If $A^2 - A + I = O$, where O is the zero matrix and I is the identity matrix, then $A^{-1}$ is

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:

If $\begin{bmatrix} x-y & 0 \\ x+y & 1 \end{bmatrix}$ is an identity matrix and $\begin{bmatrix} x & y \\ z & x \end{bmatrix}$ is a singular matrix then:

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$, the sum of the values of $\lambda$ is:

If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$, then $|A|$ is

If $A = \begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x) = x^2-2x-3$, then $f(A)$ is