Question

Give below are defined as few properties of matrices. Which of the following is not true for matrices?

• A. $AB=AC$ does not imply $B=C$
• B. $A+B=B+A$
• C. $(AB{)}^{\prime }=B^{\prime }{A}^{\prime }$
• D. $AB=0$ implies $|A|=0$ or $|B|=0$

Answer 1

The correct option is A $AB=AC$ does not imply $B=C$

$A.AB=AC$ holds true only when $A$ is a non-zero matrix.

$B.A+B=B+A$ This statement is true since matrices clearly follow the commutative law.

$C.(AB{)}^{\prime }=B^{\prime }{A}^{\prime }$

As the property of transpose of a matrix, $(AB{)}^{\prime }\ne A^{\prime }{B}^{\prime }$ but equals $B^{\prime }{A}^{\prime }$

$D.AB=0$ implies either $|A|=0$ or $|B|=0$

The product can never yield a null matrix if either of the matrices is non-zero.