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

User JiriS
by
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1 Answer

2 votes


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)=\frac12A}

User Anthony Tietjen
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6.4k points