Questions
In which of the following type of matrix inverse does not exist always
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a
idempotent
b
orthogonal
c
involutary
d
none of these
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Correct option is A
For involutary matrix, A2=I⇒A2=|I|⇒|A|2=1⇒|A|=±1 For idempotent matrix,A2=A⇒A2=|A|⇒|A|2=|A|⇒|A|=0 or 1 For orthogonal matrix, AAT=I⇒AAT=|I|⇒A∥AT=1⇒|A|2=1⇒|A|=±1 Thus if matrix A is idempotent it may not be invertible.Similar Questions
If is a matrix satisfying the equation then
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