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 what would be third element in the second column of matrix AB?

• A. -8
• B. -5
• C. 5
• D. 7

Answer 1

The correct option is A -8

We know that two matrices can be multiplied only when number of columns of A = no. of rows of B.

(for AB to be defined). In the above question the 2 matrices satisfy this condition.

Also elements of AB are obtained by adding the products of corresponding elements of $i^{th}$ row of A and $j^{th}$ column of B. This will give $(i,j{)}^{th}$ element of AB.

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

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

$=\left[\begin{array}{cc}3& -2\\ 5& -5\\ 7& -8\end{array}\right]$

So the third element of second column of this matrix will be -8 which is the correct answer.