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Mathematics
Problem
For a square matrix
A
A
A
of order
n
n
n
, suppose
2
A
+
3
I
n
=
O
2A + 3I_n = O
2
A
+
3
I
n
=
O
, where
I
n
I_n
I
n
is the identity matrix of order
n
n
n
and
O
O
O
is the corresponding zero matrix. Find the real number
k
k
k
so that
k
(
4
A
)
=
6
I
n
k(4A) = 6I_n
k
(
4
A
)
=
6
I
n
. a)
1
1
1
b)
−
2
-2
−
2
c)
−
1
-1
−
1
d)
−
1
2
-\dfrac12
−
2
1
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