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Mathematics
Mathematics
Problem
Consider the matrices
A
=
(
5
1
2
x
)
,
B
=
(
x
−
1
−
2
5
)
.
A=\begin{pmatrix}5 & 1\\ 2 & x\end{pmatrix},\quad B=\begin{pmatrix}x & -1\\ -2 & 5\end{pmatrix}.
A
=
(
5
2
1
x
)
,
B
=
(
x
−
2
−
1
5
)
.
It is given that
A
B
=
I
2
AB=I_2
A
B
=
I
2
. (i) Determine the value of
x
x
x
. (ii) Using the value of
x
x
x
found in part (i), verify that
B
A
=
I
2
BA=I_2
B
A
=
I
2
also holds.
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