For any matrices $A, B, C$
if $A B = A C$ , then we can say that $B = C$ ,
State true or false.

True

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False

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Solution

The correct option is B False
It is not necessarily true that if $A B = A C$ then $B = C$
This would only be true if it was given that A is nonsingular.
Hence the above statement is false

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State true or false:

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A B = A C

Say true or false:

Let A, B be two matrices, such that

A B = A

and

B A = B

, then

A^{2} = A

and

B^{2} = B

Q. Say true or false:

Let A, B be two matrices such that they commute, then

(A B)^{n} = A^{n} B^{n}

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For any matrices A,B,Cif AB=AC, then we can say that B=C, State true or false.

The correct option is B FalseIt is not necessarily true that if AB=AC then B=CThis would only be true if it was given that A is nonsingular.Hence the above statement is false

For any matrices $A, B, C$
if $A B = A C$ , then we can say that $B = C$ ,
State true or false.

The correct option is B False
It is not necessarily true that if $A B = A C$ then $B = C$
This would only be true if it was given that A is nonsingular.
Hence the above statement is false