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Byju's Answer
Standard XII
Mathematics
Singular and Non Singualar Matrices
34. Show that...
Question
34. Show that positive odd integral powers of a skew- symmetric matrix are skew- symmetric and positive even integral power of a skew- symmetric matrix are symmetric.
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Q.
Say true or false:
All positive odd integral powers of skew-symmetric matrix are symmetric.
Q.
Prove that +ive off integral powers of a skew asymmetric matrix are skew symmetric but +ive even integral powers are symmetric
Q.
Show that matrix
A
+
B
is symmetric or skew symmetric according as
A
and
B
are symmetric of skew symmetric.
Q.
Show that the matrix
B
′
A
B
is symmetric or skew symmetric according as
A
is symmetric or skew symmetric.
Q.
If A and B are square matrices of same order and B is a skew-symmetric matrix, show that
A
′
B
A
is a skew-symmetric matrix.
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