Choose the correct statement regarding matrices.

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

If $A = [x \quad y \quad z]$,$B = \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$,$C = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $(AB) \cdot C$ is an $m \times n$ order matrix,then:

Find the value of $x, y$ and $z$ from the following equation : $\begin{bmatrix} 4 & 3 \\ x & 5 \end{bmatrix} = \begin{bmatrix} y & z \\ 1 & 5 \end{bmatrix}$

If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then for $n \geq 1$, mathematical induction gives:

Show that $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \ne \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix}$