JEE Main | 2014MatricesMedium
Question
If A is an 3 × 3 non-singular matrix such that AA′ = A′A and B = A-1A′, then BB′ equals
Options
A.B-1
B.(B-1)′
C.I + B
D.I
Solution
BB′ = (A-1 .A′)(A(A-1)′)
= A-1 .A.A′.(A-1)1 {as AA′ = A′A}
= I(A-1A)′
= I.I = I2 = I
= A-1 .A.A′.(A-1)1 {as AA′ = A′A}
= I(A-1A)′
= I.I = I2 = I
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