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If A is a scalar matrix with scalar k 0, of order 3, then A^{-

Question

If $A$ is a scalar matrix with scalar $k \neq = 0$ , of order $3$ , then $A^{- 1}$ is:

\frac{1}{k} I

k I

\frac{1}{k ^{2}} I

\frac{1}{k ^{3}} I

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Oliver Discussed

A

is a scalar matrix with scalar

k \neq = 0

, of order

3

, then

A^{- 1}

is:

15 mins ago

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15 mins ago

Text solutionVerified

Given

A

is a scalar matrix with scalar

k \neq = 0

⟹ A = k I

We know that

A . A^{- 1} = I

⟹ (k I) . A^{- 1} = I

⟹ k I . A^{- 1} = I

⟹ I . A^{- 1} = \frac{1}{k} I

⟹ A^{- 1} = \frac{1}{k} I

(∵ A . I = A)

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Question Text	If $A$ is a scalar matrix with scalar $k \neq = 0$ , of order $3$ , then $A^{- 1}$ is:
Answer Type	Text solution:1
Upvotes	150