The Total solution for NCERT class 6-12
Find the inverse of each of the matrices, if itexists.
Answer - 11 : -
We know that A = AI
Answer - 12 : -
We know that A = IA
Now, in the above equation, we can see all thezeros in the second row of the matrix on the L.H.S.
Therefore, A−1 doesnot exist.
Answer - 13 : -
Answer - 14 : -
Applying , we have:
Now, in the above equation, we can see all thezeros in the first row of the matrix on the L.H.S.
Answer - 15 : -
Answer - 16 : -
Applying R2 → R2 +3R1 and R3 → R3 − 2R1,we have:
Answer - 17 : -
Applying, we have:
Matrices A and B willbe inverse of each other only if
A. AB = BA C. AB = 0, BA = I B. AB = BA = 0 D. AB = BA = I
Answer - 18 : -
We know that if A is asquare matrix of order m, and if there exists another squarematrix B of the same order m, such that AB = BA = I,then B is said to be the inverse of A. In thiscase, it is clear that A is the inverse of B.
Thus, matrices A and B willbe inverses of each other only if AB = BA = I.
Answer: D