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Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
If A is the given matrix, Inverse of A = adj(A)/|A|, where |A| is the determinant of A.
We know that A = AI
where |A| = ad-bc = 1
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = AI
Find the inverse of each of the matrices, if it exists.
We know that A = AI
Find the inverse of each of the matrices, if it exists.
We know that A = IA
As |A| = 0 , which means that the given matrix is a singular matrix.
And inverse only exists for non singular matrices.
Hence for the matrix, inverse does not exist.
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Find the inverse of each of the matrices, if it exists.
#
Find the inverse of each of the matrices, if it exists.
(i)
We know that A = IA
Applying
, we have:
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.
(ii)
We know that A = IA
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Applying R2→ R2 + 3R1 and R3→ R3 − 2R1, we have:
Find the inverse of each of the matrices, if it exists.
We know that A = IA
Applying
, we have:
Matrices A and B will be inverse of each other only if
A. AB = BA
C. AB = 0, BA = I
B. AB = BA = 0
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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