Search any question & find its solution
Question:
Answered & Verified by Expert
Let $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ and $B=\left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right), a, b \in N$. Then
Options:
Solution:
2017 Upvotes
Verified Answer
The correct answer is:
there exist infinitely many B’s such that AB = BA
there exist infinitely many B’s such that AB = BA
$A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] \quad B=\left[\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right]$
$A B=\left[\begin{array}{ll}a & 2 b \\ 3 a & 4 b\end{array}\right]$
$B A=\left[\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]=\left[\begin{array}{cc}a & 2 a \\ 3 b & 4 b\end{array}\right]$
$A B=B A$ only when $a=b$
$A B=\left[\begin{array}{ll}a & 2 b \\ 3 a & 4 b\end{array}\right]$
$B A=\left[\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]=\left[\begin{array}{cc}a & 2 a \\ 3 b & 4 b\end{array}\right]$
$A B=B A$ only when $a=b$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.