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If A= [[1,1,1],[1,1,1],[1,1,1]] then a...

If `A= [[1,1,1],[1,1,1],[1,1,1]]` then
a. `A^(3) = 9 A `
b. `A^(3) = 27 A `
c. `A + A = A^(2)`
d. `A^(-1)` does not exist

A

`A^(3) = 9 A `

B

`A^(3) = 27 A `

C

`A + A = A^(2)`

D

`A^(-1)` does not exist

Text Solution

Verified by Experts

The correct Answer is:
A, D
Here, `abs(A)=0`
`therefore A^(-1)` does not exist.
Now, `A^(2) = [[1,1,1],[1,1,1],[1,1,1]][[1,1,1],[1,1,1],[1,1,1]]= [[3,3,3],[3,3,3],[3,3,3]] = 3A`
`therefore A^(3) = A^(2) cdot 2 = 3 A cdot A = 3 A^(2) = 3(3A) = 9 A`
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