Matrices
Exercise 3.4
Question 1: Find the inverse of each of the matrices, if it exists.
Answer
Question 2: Find the inverse of each of the matrices, if it exists.
Answer
Question 3: Find the inverse of each of the matrices, if it exists.
Answer
Question 4: Find the inverse of each of the matrices, if it exists.
Answer
Question 5: Find the inverse of each of the matrices, if it exists.
Answer
Question 6: Find the inverse of each of the matrices, if it exists.
Question 7: Find the inverse of each of the matrices, if it exists.
Question 8: Find the inverse of each of the matrices, if it exists.
Question 9: Find the inverse of each of the matrices, if it exists.
Answer
Question 10: Find the inverse of each of the matrices, if it exists.
Answer
Question 11: Find the inverse of each of the matrices, if it exists.
Answer
Question 12: Find the inverse of each of the matrices, if it exists.
Answer
Now, in the above equation, we can see all the zeros in the second row of the matrix on
the L.H.S.
Therefore, A−1 does not exist.
Question 13: Find the inverse of each of the matrices, if it exists.
Answer
Question 14: Find the inverse of each of the matrices, if it exists.
Answer
Now, in the above equation, we can see all the zeros in the first row of the matrix on the
L.H.S.
Therefore, A−1 does not exist.
Question 16: Find the inverse of each of the matrices, if it exists.
Answer
Question 17: Find the inverse of each of the matrices, if it exists.
Answer
Question 18: Matrices A and B will be inverse of each other only if
A. AB = BA
B. AB = BA = 0
C. AB = 0, BA = I
D. AB = BA = I
Answer: D
We know that if A is a square matrix of order m, and if there exists another square matrix
B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In
this case, it is clear that A is the inverse of B.
Thus, matrices A and B will be inverses of each other only if AB = BA = I.
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