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If for a matrix A, A2+I=0 where I is the identity matrix then A=?

If for a matrix A, A2+I=0 where I is the identity matrix then A=?
 

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Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
A^2+I=0
A^-1(A^2+I)=0
A+A^-1=0
so, A= – A^-1
an important thing to note here is that hw can we be sure that A^-1 will exist. the reason is that A^2+I=0 implies that A^2= – I or taking determinant, we get [det(A)]^2= ±1, so that det(A) is surely not zero, implying the existence of A^-1.

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