Matrices — Class 12 Maths Solution

ncert misc SA NCERT,Misc,Q.No.4,Page.100
Question

If A and B are symmetric matrices, prove that AB$-$BA is a skew symmetric matrix.

Step-by-step Solution

.:

Given. : A and B are symmetric matrices, therefore $A' = A, B' = B.$

To prove :(AB$- BA)'= -$(AB$-$BA)

Proof : $(AB$ - $BA)'$=$(AB)'$ -

$(BA)$=$B'A'$ - $A'B'=BA$ - $AB =$ -

$(AB$ - $BA)$

So, AB$-$BA is a skew-symmetric matrix.

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