Let A = \(\left[\matrix{5&0\\0&-5}\right]\) then \( { A }^{ 2 } \) is equal to
Answer & explanation
Correct answer: option 1
\( { A }^{ 2 } \) = \(\left[\matrix{5&0\\0&-5}\right]\)\(\left[\matrix{5&0\\0&-5}\right]\)
\( { A }^{ 2 } \) = \(\left[\matrix{5×5 + 0×0&5×0 + 0×(-5)\\0×5 + 0×(-5)&0×0 +(-5)×(-5)}\right]\)
\( { A }^{ 2 } \) = \(\left[\matrix{25&0\\0&25}\right]\)
\( { A }^{ 2 } \) = 25\(\left[\matrix{1&0\\0&1}\right]\)