If a b and c are non zero real numbers then the inverse of the matrix a o o ...........

Mathematics (NDA) Matrices and Determinants

If a , b and c are non-zero real numbers, then the inverse of the matrix-

[ a o o ]

[ o b o ]

[ o o c ] is equal to -

[ a^-1 0 0 ]

[ 0 b^-10 ]

[ a^-1 0 0 ]

1 / abc [ 0 b^-1 0 ]

[ 0 0 c^-1]

[ 1 0 0 ]

1 / abc [ 0 1 0 ]

[ 0 0 1 ]

[ a 0 0 ]

1 / abc [ 0 b 0 ]

[ 0 0 c ]

A = [ a 0 0 ]

[ 0 b 0 ]

[ 0 0 c ]

A^-1 = 1 / |A| [ a^-1 0 0 ]

[ 0 b^-1 0 ]

[ 0 0 c^-1 ]

And |A| = abc

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