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If-A-is-an-involutory-matrix-then-I-A-I-A-0-




Question Number 55844 by gunawan last updated on 05/Mar/19
If A is an involutory matrix, then   (I+A)(I−A)=0.
IfAisaninvolutorymatrix,then(I+A)(IA)=0.
Answered by 121194 last updated on 05/Mar/19
a involutory matrix is a matrix that is it own inverse  A^2 =I  (I+A)(I−A)=I^2 −IA+AI−A^2   =I^2 −I  =0
ainvolutorymatrixisamatrixthatisitowninverseA2=I(I+A)(IA)=I2IA+AIA2=I2I=0

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