Question
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
✓
Answer
Order of $A=a \times(a+3)$
Order of $B=b \times(17-b)$
Given: Product of $A B$ exist
$
\begin{aligned}
& a+3=b \\
& a-b=-3
\end{aligned}
$
Product of BA exist
$
\begin{aligned}
& 17-b=a \\
& -a-b=-17 \\
& a+b=17 \ldots \ldots . .(2) \\
& (1)+(2) \Rightarrow 2 a=14 \\
& a=\frac{14}{2}=7
\end{aligned}
$
Substitute the value of $a =7$ in (1)
$
7-b=-3 \Rightarrow-b=-3-7
$
– b = – 10 ⇒ b = 10
The value of a = 7 and b = 10
Order of $B=b \times(17-b)$
Given: Product of $A B$ exist
$
\begin{aligned}
& a+3=b \\
& a-b=-3
\end{aligned}
$
Product of BA exist
$
\begin{aligned}
& 17-b=a \\
& -a-b=-17 \\
& a+b=17 \ldots \ldots . .(2) \\
& (1)+(2) \Rightarrow 2 a=14 \\
& a=\frac{14}{2}=7
\end{aligned}
$
Substitute the value of $a =7$ in (1)
$
7-b=-3 \Rightarrow-b=-3-7
$
– b = – 10 ⇒ b = 10
The value of a = 7 and b = 10
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