Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

If $A=\left[\begin{array}{lll}-2 & 3 & -1 \\ -1 & 2 & -1 \\ -6 & 9 & -4\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 3 & -1 \\ 2 & 2 & -1 \\ 3 & 0 & -1\end{array}\right]$, then

Options:

AB = BA

AB ≠ BA

AB = 1/2 BA

None of these

Correct Answer:

AB = BA

Explanation:

$AB =\left[\begin{array}{lll}-2 & 3 & -1 \\ -1 & 2 & -1 \\ -6 & 9 & -4\end{array}\right]\left[\begin{array}{lll}1 & 3 & -1 \\ 2 & 2 & -1 \\ 3 & 0 & -1\end{array}\right]$

$=\left[\begin{array}{ccc}-2+6-3 & -1+4-3 & -6+18-12 \\ -6+6+0 & -3+4+0 & -18+18+0 \\ 2-3+1 & 1-2+1 & 6-9+4\end{array}\right]=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

$BA =\left[\begin{array}{lll}1 & 3 & -1 \\ 2 & 2 & -1 \\ 3 & 0 & -1\end{array}\right]\left[\begin{array}{lll}-2 & 3 & -1 \\ -1 & 2 & -1 \\ -6 & 9 & -4\end{array}\right]$

$=\left[\begin{array}{ccc}-2+6-3 & -4-2+6 & -6+0+6 \\ 3+6-9 & 6+4-9 & 9+0-9 \\ 6-6+0 & -2-2+4 & -3+0+4\end{array}\right]=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \Rightarrow A B=B A$

Hence (1) is the correct answer.