Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If $A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]$ then product AB is :

Options:

Not possible

$\left[\begin{array}{ccc}1 & -6 & 6 \\ 8 & -8 & 16\end{array}\right]$

$\left[\begin{array}{c}9 \\ 19 \\ 15\end{array}\right]$

$\left[\begin{array}{cc}1 & 18 \\ 10 & 16\end{array}\right]$

Correct Answer:

$\left[\begin{array}{cc}1 & 18 \\ 10 & 16\end{array}\right]$

Explanation:

$A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]$

$B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]$

$A B=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]$

$=\left[\begin{array}{cc}1-6+6 & -2+8+12 \\ -4+6+8 & 8-8+16\end{array}\right]$

$=\left[\begin{array}{cc}1 & 18 \\ 10 & 16\end{array}\right]$