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3 and 4 .Determinants and Matrices
normal
If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined, then
A
$A$and $B$ are two matrices not necessarily of same order
B
$A$ and $B$ are square matrices of same order
C
Number of columns of $A=$ Number of rows of $B$
D
None of these
Solution
(b) $A + B$ is defined $⇒$ $A$ and $B$ are of same order
Also $AB$ is defined $⇒$ Number of columns in $A$
= Number of rows in $B$
Obviously, both simultaneously mean that the matrices $A$ and $B$ are square matrices of same order.
Standard 12
Mathematics
