If A is an invertible matrix, then which of the following is not true
(a) ${(A^{2})}^{- 1} = {(A^{- 1})}^{2}$
(b) $|A^{- 1}| = {|A|}^{- 1}$
(c) ${(A^{T})}^{- 1} = {(A^{- 1})}^{T}$
(d) $|A| \neq 0$

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Solution

(a) ${(A^{2})}^{- 1} = {(A^{- 1})}^{2}$

We have, $|A^{- 1}| = {|A|}^{- 1}$ , ${(A^{T})}^{- 1} = {(A^{- 1})}^{T}$ and $|A| \neq 0$ all are the properties of the inverse of a matrix A

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