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Byju's Answer
Standard XII
Mathematics
Skew Symmetric Matrix
prove that su...
Question
prove that sum of two skew symmetric matrices is a skew symmetric matrix
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Solution
Let
A
and
B
are
2
skew
symmetric
matrices
.
Now
,
A
'
=
-
A
and
B
'
=
-
B
Now
,
A
+
B
'
=
A
'
+
B
'
=
-
A
-
B
=
-
A
+
B
Hence
,
A
+
B
is
a
skew
symmetric
matrix
.
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Similar questions
Q.
Prove that any square matrix
A
can be expressed as the sum of two symmetric and skew-symmetric matrices.
Q.
The sum of two skew-symmetric matrices is always __________ matrix.
Q.
If
A
and
B
are symmetric matrices, prove that
AB
ā
BA
is a skew symmetric matrix.
