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Mathematics
Mathematics
Problem
Given
A
=
(
2
3
1
2
)
A=\begin{pmatrix}2 & 3\\ 1 & 2\end{pmatrix}
A
=
(
2
1
3
2
)
and
B
=
(
p
−
3
q
2
)
B=\begin{pmatrix}p & -3\\ q & 2\end{pmatrix}
B
=
(
p
q
−
3
2
)
, determine the values of
p
p
p
and
q
q
q
so that
A
A
A
and
B
B
B
are mutual inverses, and verify your result. a. (i) Find
p
p
p
and
q
q
q
such that
A
B
=
I
2
AB=I_2
A
B
=
I
2
. b. (ii) Using the values of
p
p
p
and
q
q
q
, show that
B
A
=
I
2
BA=I_2
B
A
=
I
2
.
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