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Determinants

Question

If A is a 3x3 non- singular matrix such that AA^T = A^TA, then BB^T is equal to

l +B
l

B^-1

(B^-1)^T

Solution

If A is non - singular matrix then |A| ≠0
AA^T = A^TA and B = A^-1A^T
BB^T = (A^-1A^T)(A^-1A^T)^T
= A^-1A^TA(A^-1)^T [∵ (AB)^T= B^TA^T]
=A^-1AA^T(A^-1)^T [∵ AA^T = A^TA]
=A^T(A^-1)^T [ ∵A^-1A = l]
=A^-1A)^T [∵ (AB)^T = B^TA^T]
l^T = l

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Determinants

If A is a 3x3 non- singular matrix such that AA^T = A^TA, then BB^T is equal to

l +B
l

B^-1

(B^-1)^T

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Determinants

If A is a 3x3 non- singular matrix such that AAT = ATA, then BBT is equal to l +B l B-1 (B-1)T

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If A is a 3x3 non- singular matrix such that AA^T = A^TA, then BB^T is equal to

l +B
l

B^-1

(B^-1)^T