First slide

Transpose of matrix

Question

If A and B two are 3x3 matrices, then which one of following is not true:

Easy

A

$(A + B)^{'} = A^{'} + B^{'}$
B

$(A B)^{'} = A^{'} B^{'}$
C

$\det (A B) = \det (A) \det (B)$
D

$A (adj A) = | A | I_{3}$

Solution

If A and B are two 3x3 matrices, then
$(A B)^{'} = B^{'} A^{'}$ [Reversal Law]
and not $(A B)^{'} = A^{'} B^{'}$ .

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