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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Similar questions

Show that if A and B are square matrices such that AB = BA, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ .

A, B a n d C

A B = A C \Rightarrow B = C

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