Search
Engineering
Mathematics
Algebra of Matrices
Multiplication of Matrices
Question

Show that AB ≠ BA in the following matrices:
A=[ 10−4−1−11 509 −50] and B= [1 213 421 32].

LiveFree JEE Main Previous Year Online PapersLive Free JEE Advance Previous Year Online Papers
JEE Advance
College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

START NOW
Solution
Verified BY
Verified by Zigyan
L.H.S =AB=[10−4−1−11509−50]3×3[121342132]3×3.
AB=[10−12−120−16−310−8−2−11+15+0−22+20+0−11+10+09−15+018−20+09−10+0]3×3
∴ AB=[−3104−2−1−6−2−1]3×3           .........(1)
R.H.S =BA=[121342132]3×3[10−4−1−11509−50]3×3
BA=[10−22+9−4+10−5−1+0+030−44+18−12+20−10−3+0+010−33+18−4+15−10−1+0+0]3×3
=[−31−14−2−3−51−1]3×3            ..........(2)
From (1) and (2) we have L.H.S ≠ R.H.S
Hence AB ≠ BA
Hence proved.
Was this answer helpful?
This website uses cookies. By Using our website you agree to our Cookies Policy