If M is a matrix of order $$3X3$$ such that $$MMT=I$$ and det $$(M)=1$$ then detM−$$I=$$

Question

If M is a matrix of order $$3X3$$ such that $$MMT=I$$ and det $$(M)=1$$ then detM−$$I=$$

Infinity Learn · Accepted Answer

We have |$$M-I$$|$$=M-MMT$$                             $$=MI-MT$$                             $$=$$|M|$$I-MT$$                             $$=$$|(I-M)T$$| ∵$$M=1and$$ $$IT=I$$                             $$=$$|$$(I-M)|    ∵$$AT=A$$                            $$=(-1)3$$|$$M-I$$|.           ∴ $$M-I=-$$|$$M-I$$|.⇒$$2$$|$$M-I$$|$$=0$$.⇒|$$M-I$$|$$=0$$.

If M is a matrix of order $3 X 3$ such that $M M^{T} = I$ and det (M) $= 1$ then det $(M - I) =$

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If M is a matrix of order 3X3 such that MMT=I and det (M)=1 then detM−I=

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If M is a matrix of order $3 X 3$ such that $M M^{T} = I$ and det (M) $= 1$ then det $(M - I) =$