Question

let A and B are square matrices such that AB=I then zero is an eigen value of​

Answer 1

Answer:

Both A and B

Step-by-step explanation:

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Answer 2

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PROPERTY TO BE IMPLEMENTED

The product of the eigen values of a matrix P is equal to its determinant

GIVEN

Let A and B are square matrices such that AB = I

TO DETERMINE

Zero is an eigen value of

CALCULATION

Since A and B are square matrices such that AB = I

$\implies{ \sf{ |AB \: | \: }}= | I |$

$\implies{ \sf{ |A | \: | B \: | = 1 \: }}$

$\implies{ \sf{ both \: \: of \: |A | \: and \: \: | B | \:are \: non - zero \: }}$

We know that The product of the eigen values of a matrix A is equal to its determinant

Since determinant value of both A and B are non-zero

Hence zero Can not be a eigen value of A and B