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If for a matrix A, A2+I=0 where I is the identity matrix then A=?
A^2+I=0A^-1(A^2+I)=0A+A^-1=0so, A= – A^-1an 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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