If `A` is an invertible matrix, then `(a d jdotA^(-1))` is equal to a.`[a d jdot(A^(-1))]` b. `A/(d e tdotA)` c. `A` d. `(detA)A`

Options

A. adj. `(A^(-1))`
B. `A/("det. A")`
C. `A`
D. (det. A) A

Explanation

`A^(-1)=("adj (A)")/(|A|)`
`:. ("adj A")^(-1)=("adj (adj A)")/(|"adj A"|)`
`=(|A|^(n-2) A)/(|A|^(n-1))`
`=A/(|A|)`
Also A (adj A) `=|A|I`
or `A^(-1) ("adj "A^(-1))=|A^(-1|I`
or `A^(-1) ("adj "A^(-1))=I/(|A|)`
or `A A^(-1) ("adj "A^(-1))=(A.I)/(|A|)`
or `I ("adj "A^(-1))=A/(|A|)`
or `("adj "A^(-1))=A/(|A|)=("adj "A)^(-1)`