[(1 2), (3 4)] [(1 0), (0 1)] =

Question

\(\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] \left[\begin{array}{ll}1 & 0 \\ 0 & 1 \end{array}\right]=\)

(A) \(\left[\begin{array}{rr}1 & 0 \\ 0 & 4\end{array}\right]\)

(B) \(\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]\)

(C) \(\left[\begin{array}{ll}1 & 2 \\ 0 & 4\end{array}\right]\)

(D) \(\left[\begin{array}{ll}1 & 2 \\ 3 & 0\end{array}\right]\)

Answer 1

Correct option is (B) \(\begin{bmatrix} 1&2\\3&4\end {bmatrix}\) 

\(\begin{bmatrix} 1&2\\3&4\end {bmatrix} \begin{bmatrix} 1&0\\0&1\end {bmatrix} \)

\(= \begin{bmatrix}(1 \times 1) + (2\times 0)&(1 \times 0) + (2 \times 1)\\(3 \times 1)+(4 \times 0)&(3 \times 0)+ (4\times 1) \end {bmatrix}\)

\(= \begin{bmatrix}1 + 0&0+2\\3 +0&0+4\end {bmatrix}\)

\(=\begin{bmatrix} 1&2\\3&4\end {bmatrix}\)

Answer 2

Correct option is (B) \(\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]\)