A is an involutory matrix given by then the inverse of will be

Engineering

Mathematics

Special Type of Square Matrices

Inverse of a Matrix

Question

A is an involutory matrix given by $A = [\begin{array}{ccc} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{array}]$ then the inverse of $\frac{A}{2}$ will be

A²

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

$\frac{A}{2}$

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Given A to be involutory matrix, then according to the definition of involutory matrix we have, A² = I. [ I being identity matrix of order 3].

So,

A² = I

or, A = A^–1 [ Since involutory matrix is always invertible]

or,

\frac{A}{2} = \frac{A^{- 1}}{2}