If A = [(1,-1)(2,-1)] , B = [(a,1)(b,-1)] and (A + B)^2 = A^2 + B^2, then values of a and b are : A. a = 4, b = 1 B. a = 1, b = 4 ​

Question

If A = \(\begin{bmatrix} 1&-1 \\[0.3em] 2 & -1 \\[0.3em] \end{bmatrix}\), B = \(\begin{bmatrix} a&1 \\[0.3em] b & -1 \\[0.3em] \end{bmatrix}\) and (A + B)² = A² + B², then values of a and b are :

A. a = 4, b = 1 

B. a = 1, b = 4 

C. a = 0, b = 4 

D. a = 2, b = 4

Answer 1

 (B). a = 1, b = 4 

A + B = \(\begin{bmatrix} 1&-1 \\[0.3em] 2 & -1 \\[0.3em] \end{bmatrix}\)+\(\begin{bmatrix} a&1 \\[0.3em] b & -1 \\[0.3em] \end{bmatrix}\) 

a² = 1 & b = 4 

a = ± 1

Hence, 

Option (B) is the correct answer.