If a, b, c are non-zero real numbers, then the inverse of the matrix `A=[{:(a,0,0),(0,b,0),(0,0,c):}]`is equal to

Options

A. `[{:(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1)):}]`
B. `(1)/(abc)[{:(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1)):}]`
C. `(1)/(abc)[{:(1,0,0),(0,1,0),(0,0,1):}]`
D. `(1)/(abc)[{:(a,0,0),(0,b,0),(0,0,c):}]`

Answer

A

Explanation

`A=[{:(a,0,0),(0,b,0),(0,0,c):}]`
`A^(-1)=[{:((1)/(a),0,0),(0,(1)/(b),0),(0,0,(1)/(c)):}]=[{:(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1)):}]`