Question

If A is a non- singular matrix, then A(adj A) =​

Answer 1

Answer:

If A is a non singular square matrix; then adj(adjA) = |A|^(n-2)

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Answer 2

Answer:

A(adjA) = |A|.

Step-by-step explanation:

Given,

A is a non - singular matrix

To find,

A(adjA).....(1)

We know that if A is non-singular matrix then its inverse exists

i.e. |A| ≠ 0

So, inverse of A is given by

A⁻¹ = adj(A)/|A|

⇒ adj(A) = |A|(A⁻¹ )....(2)

Now putting equation (1) in (2)

⇒ A(|A|(A⁻¹ ))

⇒ (AA⁻¹ )(|A|)

⇒ |A|

Therefore, A(adjA) = |A|.

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