Questions
The inverse of a diagonal matrix is
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a
a diagonal matrix
b
a skew –symmetric matrix
c
a symmetric matrix
d
none of these
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Correct option is A
A=diagd1,d2,d3,……dn⇒|A|=d1×d2×d3×d4……….dnNow, Cofactor of d1 is d2d3....dn Cofactor of d2 is d1×d3×d4......dn Cofactor of d3is d1×d2×d4......dn Cofactor of dn is d1×d2×d3……dn−1⇒ A−1=1|A|adj A=diagd1−1,d2−1,d3−1,......dn−1 Hence A−1 is also a diagonal matrix.Similar Questions
If is a matrix satisfying the equation then
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