isi-entrance 2022 Q5

isi-entrance · India · UGA 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning

Let $A$ and $B$ be two $3 \times 3$ matrices such that $( A + B ) ^ { 2 } = A ^ { 2 } + B ^ { 2 }$. Which of the following must be true?
(A) $A$ and $B$ are zero matrices.
(B) $A B$ is the zero matrix.
(C) $( A - B ) ^ { 2 } = A ^ { 2 } - B ^ { 2 }$
(D) $( A - B ) ^ { 2 } = A ^ { 2 } + B ^ { 2 }$

Let $A$ and $B$ be two $3 \times 3$ matrices such that $( A + B ) ^ { 2 } = A ^ { 2 } + B ^ { 2 }$. Which of the following must be true?\\
(A) $A$ and $B$ are zero matrices.\\
(B) $A B$ is the zero matrix.\\
(C) $( A - B ) ^ { 2 } = A ^ { 2 } - B ^ { 2 }$\\
(D) $( A - B ) ^ { 2 } = A ^ { 2 } + B ^ { 2 }$

Paper Questions

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