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Mathematics
Mathematics
Problem
Let
A
A
A
be a square matrix such that
A
A
T
=
I
AA^T = I
A
A
T
=
I
. Then
1
2
A
[
(
A
+
A
T
)
2
+
(
A
−
A
T
)
2
]
\frac{1}{2}A[(A+A^T)^2 + (A-A^T)^2]
2
1
A
[(
A
+
A
T
)
2
+
(
A
−
A
T
)
2
]
is equal to (Main 29th Jan 1st Shift 2024) (a)
A
2
+
A
T
A^2 + A^T
A
2
+
A
T
(b)
A
2
+
I
A^2 + I
A
2
+
I
(c)
A
3
+
I
A^3 + I
A
3
+
I
(d)
A
3
+
A
T
A^3 + A^T
A
3
+
A
T
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