Question

If $A=\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 2& 3& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& -2\\ -1& 0\\ 2& -1\end{array}\right]$, then third element in the second column of matrix $AB$ is

• A. 0.0
• B. 9
• C. 8
• D. $-8$

Answer 1

The correct option is D $-8$

We know that two matrices can be multiplied only when number of columns of A = number of rows of B.

Elements of $AB$ are obtained by adding the products of corresponding elements of $i^{th}$ row of A and $j^{th}$ column of B.

So, $\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 2& 3& 4\end{array}\right]\left[\begin{array}{cc}-1& -2\\ -1& 0\\ 2& -1\end{array}\right]$

$=\left[\begin{array}{cc}(0\times -1)+(1\times -1)+2\times 2& (0\times -2)+(1\times 0)+(2\times -1)\\ (1\times -1)+(2\times -1)+3\times 2& (1\times -2)+(2\times 0)+(3\times -1)\\ (2\times -1)+(3\times -1)+4\times 2& (2\times -2)+(3\times 0)+(4\times -1)\end{array}\right]$

$=\left[\begin{array}{cc}3& -2\\ 3& -5\\ 3& -8\end{array}\right]$
So, third element of second column of this matrix is $-8$