Question

$A$ and $B$ are two matrices of same order $3\times 3$, where $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 5& 6& 8\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& 2& 5\\ 2& 3& 8\\ 7& 2& 9\end{array}\right]4$. Find AB

Answer 1

Given that,

$\begin{array}{c}A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 5& 6& 8\end{array}\right],B=\left[\begin{array}{ccc}3& 2& 5\\ 2& 3& 8\\ 7& 2& 9\end{array}\right]4\\ =\left[\begin{array}{ccc}12& 8& 20\\ 8& 12& 32\\ 28& 8& 36\end{array}\right]\\ AB=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 5& 6& 8\end{array}\right]\left[\begin{array}{ccc}12& 8& 20\\ 8& 12& 32\\ 28& 8& 36\end{array}\right]\\ =\left[\begin{array}{ccc}12+16+34& 8+24+24& 20+64+108\\ 24+24+112& 16+36+32& 40+96+149\\ 60+48+224& 40+72+64& 100+192+288\end{array}\right]\\ =\left[\begin{array}{ccc}112& 56& 142\\ 160& 84& 280\\ 332& 176& 540\end{array}\right]\end{array}$