The Total solution for NCERT class 6-12
Matrices┬аA┬аand┬аB┬аwillbe inverse of each other only if
A.┬аAB┬а=┬аBA┬а ┬а C.┬аAB┬а= 0,┬аBA┬а=┬аI┬а ┬а ┬а ┬а ┬аB.┬аAB┬а=┬аBA┬а= 0┬а ┬а ┬аD.┬аAB┬а=┬аBA┬а=┬аI
We know that┬аif┬аA┬аis asquare matrix of order┬аm, and if there exists another squarematrix┬аB┬аof the same order┬аm, such that┬аAB┬а=┬аBA┬а=┬аI,then┬аB┬аis said to be the inverse of┬аA. In thiscase, it is clear that┬аA┬аis the inverse of┬аB.
Thus, matrices┬аA┬аand┬аB┬аwillbe inverses of each other only if┬аAB┬а=┬аBA┬а=┬аI.
Answer: D