If A and B are square matrices of same order show that AB^T-BA^T

CBSE Class 12 CBSE Class 12 Maths
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1

if A and B are square matrices of same order show that AB^T-BA^T is a skew symmetric matrix

2

Consider any two distinct matrices of order 2 or 3

find AB and BA also find transpose of both.

Now find transpose AB - transpose of BA you will get matrix show that transpose of that matrix is multiplied by minus sign of original matrix. Hence it is a skwe symmetric matrix.