Question:
Two matrices A and B are multiplicative inverse of each other only if
Two matrices A and B are multiplicative inverse of each other only if
Updated On: Apr 19, 2023
- $AB = 0, BA = I$
- $AB = BA = 0$
- $AB = BA$
- $AB = BA = I$
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The Correct Option is D
Solution and Explanation
A and B are inverses of each other iff
$AB = BA = I$.
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Notes on Invertible Matrices
Concepts Used:
Invertible matrices
A matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions is known as an invertible matrix. Any given square matrix A of order n × n is called invertible if and only if there exists, another n × n square matrix B such that, AB = BA = In, where In is an identity matrix of order n × n.
For example,
It can be observed that the determinant of the following matrices is non-zero.
