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If A, B, and C are three square matrices...

If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then

A

`|A| ne 0`

B

A is invertible

C

A may be orthogonal

D

A is symmetric

Text Solution

Verified by Experts

If `|A| ne 0`, then
`AB=AC`
or `A^(-1) AB=A^(-1) AC`
or `B=C`
Also, if A is orthogonal matrix, then `A A^(T)=I`
`implies |A A^(T)|=1 implies |A|^(2)=1implies` is invertible
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