jee-main 2014 Q77

jee-main · India · 06apr Matrices Matrix Algebra and Product Properties

If $A$ is a $3 \times 3$ non-singular matrix such that $A A ^ { \prime } = A ^ { \prime } A$ and $B = A ^ { - 1 } A ^ { \prime }$, then $B B ^ { \prime }$ equals, where $X ^ { \prime }$ denotes the transpose of the matrix $X$.
(1) $B ^ { - 1 }$
(2) $\left( B ^ { - 1 } \right) ^ { \prime }$
(3) $I + B$
(4) $I$

If $A$ is a $3 \times 3$ non-singular matrix such that $A A ^ { \prime } = A ^ { \prime } A$ and $B = A ^ { - 1 } A ^ { \prime }$, then $B B ^ { \prime }$ equals, where $X ^ { \prime }$ denotes the transpose of the matrix $X$.\\
(1) $B ^ { - 1 }$\\
(2) $\left( B ^ { - 1 } \right) ^ { \prime }$\\
(3) $I + B$\\
(4) $I$

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