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Q54E

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Found in: Page 109

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# TRUE OR FALSE?The formula rref(AB) = rref(A) rref(B) holds for all ${\mathbit{n}}{\mathbf{×}}{\mathbit{p}}$ matrices A and for all ${\mathbit{p}}{\mathbf{×}}{\mathbit{m}}$ matrices .

The given statement is true.

See the step by step solution

## Step 1: Reduce row echelon form

The reduced row echelon form of a matrix contains leading ones followed by zeros in each row with a shift in place of leading ones with every next row.

## Step 2: Consider the parameters

The product of rref of matrices will result in either identity matrix or the identity matrix followed by rows of zeros.

Thus, the formula rref(AB) = rref (A) rref(B) holds good.

Hence, the statement is true.