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Standard X

Mathematics

Equality of Matrices

Matrices A an...

Question

Matrices $A$ and $B$ will be inverse of each other only if

A B = B A = I

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A B = 0, B A = I

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A B = B A = 0

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A B = B A

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Solution

The correct option is A $A B = B A = I$
Given: $A$ and $B$ will be inverse of each other i.e.
$A^{- 1} = B$ and $B^{- 1} = A$
We know that
$A A^{- 1} = I$
$\Rightarrow A B = I \dots (i)$
Also,
$B B^{- 1} = I$
$\Rightarrow B A = I \dots (i i)$
From $(i)$ and $(i i)$
$A B = B A = I$
So, the correct answer is $D$

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Similar questions

Q. 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

Choose the correct answer in the following question.
Matrices A and B will be inverse of each other only if
(a)AB=BA
(b)AB =BA =O
(c)AB=O, BA=I
(d)AB=BA =I

Q. Assertion : If

A

is a non-singular matrix, then

| A^{-} 1 | = \frac{1}{| A |}

Reason : If

A

and

B

are inverse matrices of each other , then

A B = B A = I

and

| A B | = | A | | B |

Find the inverse of each of the matrices, if it exists.

Q. Find the inverse of each of the matrices , if it exists.

[\begin{matrix} 2 & 1 1 & 1 \end{matrix}]

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Equality of Matrices

Standard X Mathematics

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Matrices A and B will be inverse of each other only if

The correct option is A AB=BA=IGiven: A and B will be inverse of each other i.e. A−1=B and B−1=A We know that AA−1=I ⇒AB=I ⋯(i) Also, BB−1=I ⇒BA=I ⋯(ii) From (i) and (ii) AB=BA=I So, the correct answer is D

Matrices $A$ and $B$ will be inverse of each other only if