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LenaWriter [7]
3 years ago
8

If A is a square matrix such that A^2=2I,then A^-1=?​

Mathematics
1 answer:
Afina-wow [57]3 years ago
3 0

A^2=2I

Recall that I=AA^{-1}=A^{-1}A, so

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

Multiply on the right by A^{-1} and regroup terms:

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

A(AA^{-1})=2A^{-1}(AA^{-1})

A=2A^{-1}

and finally solve for A^{-1}:

\boxed{A^{-1}=\dfrac12A}

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