If A=1 23 4 and B=a 00 b,a,b∈N , then

A=1 23 4,B=a 00 b ⇒ AB=a2b3a4band BA=a 00 b1 23 4=a2a3b4bHence, AB = BA only when a = b

If A=1 23 4 and B=a 00 b,a,b∈N , then

A=1 23 4,B=a 00 b ⇒ AB=a2b3a4band BA=a 00 b1 23 4=a2a3b4bHence, AB = BA only when a = b

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $A = (\begin{array}{ll} 1 2 \\ 3 4 \end{array}) and B = (\begin{array}{ll} a 0 \\ 0 b \end{array}), a, b \in N$ , then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

there cannot exist any B such that AB = BA

there exist more than one but finite number of B's such that AB = BA

there exists exactly one B such that AB = BA

there exist infinitely among B’s such that AB = BA

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$A = (\begin{array}{ll} 1 2 \\ 3 4 \end{array}), B = (\begin{array}{ll} a 0 \\ 0 b \end{array}) \Rightarrow A B = (\begin{array}{cc} a & 2 b \\ 3 a & 4 b \end{array})$

and $B A = (\begin{array}{ll} a 0 \\ 0 b \end{array}) (\begin{array}{ll} 1 2 \\ 3 4 \end{array}) = (\begin{array}{cc} a & 2 a \\ 3 b & 4 b \end{array})$