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Chapter 2: Q60E (page 109)

TRUE OR FALSE?

If A is an invertible2脳2 matrix and B is any 2脳2 matrix, then the formula rref (AB) = rref (B)must hold.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Consider the parameters

The matrix A is said to be invertible, if rref (A) =I2.

Consider the matrices A,B .

02

Consider the condition

The condition is, rref (AB) = rref (B)


As rref (A)= I2, so,

rrefAB=rref(A).rref(B)鈬�rrefAB=I2.rrefB鈭�rrefAB=rrefB

Hence, the given statement is true.

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