If A- B- C are three square matrices such that A B-A C implies B-C- then the matrix A is always a - a nA- Singular matrixB- Non-singular matrixC- Orthogonal matrixD- Diagonal matrix

The correct option is B Non singular matrixAB = AC ⇒ B = C If A^ 1 exists ⇔ A is a non singular matrix. ...

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Standard IX

Mathematics

Inverse of a Matrix

If A, B, C ar...

Question

If A,B,C are three square matrices such that AB = AC implies B = C, then the matrix A is always a/an

Singular matrix

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Non-singular matrix

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Orthogonal matrix

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Diagonal matrix

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Solution

The correct option is B Non-singular matrix
$A B = A C \Rightarrow B = C$
If $A^{- 1}$ exists $\Leftrightarrow A$ is a non-singular matrix.

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If A,B,C are three square matrices such that AB = AC implies B = C, then the matrix A is always a/an

The correct option is B Non-singular matrixAB=AC⇒B=C If A−1 exists ⇔ A is a non-singular matrix.

The correct option is B Non-singular matrix
$A B = A C \Rightarrow B = C$
If $A^{- 1}$ exists $\Leftrightarrow A$ is a non-singular matrix.