If A =\(\begin{pmatrix} 2& 1\\ 2& 3 \\ 1 & 2\end{pmatrix}\) and B =\(\begin{pmatrix} 3& 2\\ 4& 2\end{pmatrix}\). Find AB
A. \(\begin{pmatrix} 18& 6\\ 12& 10 \\ 10 & 6\end{pmatrix}\) B. \(\begin{pmatrix} 10& 6\\ 13& 10 \\ 12 & 6\end{pmatrix}\) C. \(\begin{pmatrix} 10& 6\\ 12& 10 \\ 11 & 6\end{pmatrix}\) D. \(\begin{pmatrix} 10& 6\\ 18& 10 \\ 11 & 6\end{pmatrix}\)
Correct Answer: D
Explanation
Given A =\(\begin{pmatrix} 2& 1\\ 2& 3 \\ 1 & 2\end{pmatrix}\) and B =\(\begin{pmatrix} 3& 2\\ 4& 2\end{pmatrix}\). We can multiply these matrices since the number of colums in A = number of rows in B
AB =\(\begin{pmatrix} (2*3)+(1*4)&(2*2)+(1*2) \\ (2*3)+(3*4) & (2*2)+(3*2) \\ (1*3)+(2*4) &(1*2)+(2*2)\end{pmatrix}\)
AB =\(\begin{pmatrix} (6+4)& (4+2)\\ (6+12)& (4+6)\\ (3+8)& (2+4)\end{pmatrix}\)
