Question

If $A=\left[\begin{array}{rrr}1 & 2 & -1 \\ 3 & 0 & 2 \\ 4 & 5 & 0\end{array}\right], B=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$, then $A B$ is

(A) $\left[\begin{array}{rrr}5 & 1 & -3 \\ 3 & 2 & 6 \\ 14 & 5 & 0\end{array}\right]$

(B) $\left[\begin{array}{ccc}11 & 4 & 3 \\ 1 & 2 & 3 \\ 0 & 3 & 3\end{array}\right]$

(C) $\left[\begin{array}{lll}1 & 8 & 4 \\ 2 & 9 & 6 \\ 0 & 2 & 0\end{array}\right]$

(D) $\left[\begin{array}{lll}0 & 1 & 2 \\ 5 & 4 & 3 \\ 1 & 8 & 2\end{array}\right]$

Answer 1

$ \therefore A B=\left[\begin{array}{rrr}1 & 2 & -1 \\ 3 & 0 & 2 \\ 4 & 5 & 0\end{array}\right]\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]=\left[\begin{array}{rrr}5 & 1 & -3 \\ 3 & 2 & 6 \\ 14 & 5 & 0\end{array}\right]$

So, The correct option is (A).