engineering recuitment GATE IN Test Series 2023-24 Mock Test Engineering Mathematics Linear Algebra Matrix Algebra
For real constants, a and b, let \(M = \left[ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 2 }}}\\ a&b \end{array}} \right]\) be an orthogonal matrix. Then which of the following statements is/are always TRUE?
1
a + b = 0
2
\(b = \sqrt {1 - {a^2}}\)
3
ab = -1/2
4
M2 = I2