First slide

Transpose of matrix

Question

If A is symmetric as well as skew symmetric matrix, then A is

Moderate

A

diagonal
B

null
C

triangular
D

none of these

Solution

Let A = [a_ij]
Since A is skew-symmetric,
$∴$ a_ii = 0 and a_ij = –a_ji (i ≠ j)
A is symmetric as well, so a_ij = a_ji for all i and j.
$∴$ a_ij = 0 for all i ≠ j
Hence, a_ij = 0 for all i and j i.e. A is a null matrix.

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