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Maths-

General

Easy

Question

A is an involutary matrix given by A = $open square brackets table row 0 1 cell – 1 end cell row 4 cell – 3 end cell 4 row 3 cell – 3 end cell 4 end table close square brackets$ then inverse of $fraction numerator A over denominator 2 end fraction$ will be

2A
$\frac{A^{- 1}}{2}$
$\frac{A}{2}$
A²

hint Hint:

inverse of A exists.

The correct answer is: 2A

A^-1/2

We know that an involutary matrix is one which follows the property A²= I, I = identity matrix of 3^rd order.
This means that A= A^-1
A/2 = A^-1/2
Inverse of A/2 = A^-1/2, since inverse of A/2 exists.

an involutary matrix is one which follows the property A2= I, I = identity matrix of 3rd order.

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