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Question: If D = diag [d<sub>1</sub>, d<sub>2</sub>, .....d<sub>n</sub>] is a diagonal matrix with d<sub>i</s...

If D = diag [d1, d2, .....dn] is a diagonal matrix with

di ¹ 0, i = 1, 2, 3,......, n, then D–1 is

A

d11\mathrm { d } _ { 1 } ^ { - 1 } d21d_{2}^{- 1}......dn1d_{n}^{- 1}In

B

diag [dn1d_{n}^{- 1},dn11d_{n - 1}^{- 1}, ....... d11d_{1}^{- 1}]

C

diag [d11\mathrm { d } _ { 1 } ^ { - 1 } d21d_{2}^{- 1}......dn1d_{n}^{- 1}]

D

None of these

Answer

diag \mathrm { d } _ { 1 } ^ { - 1 }$$d_{2}^{- 1}$......$d_{n}^{- 1}

Explanation

Solution

Here |D| = d1d2d3 ........dn and

adj D = [d2d3 ........dn, d1d3.........dn, ........ d1d2.......dn–1]

Ž D–1 = diag [d11d_{1}^{- 1},d21d_{2}^{- 1}....... dn1d_{n}^{- 1}]