If A = bmatrix1 & -1 \\ 2 & -1bmatrix, B = bmatrixa & 1 \\ b & -1bmatrix and (A + B)^2 = A^2 + B^2 then Option 1: a = 1, b = 4 Option 2: a = -1, b = 4 Option 3: a = 2, b = -3 Option 4: a = 1, b = -4

The answer is 'a = 1, b = 4'. View full solution:

Algebra > Matrices & Determinants

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If $A = \begin{bmatrix}1 & -1 \\ 2 & -1\end{bmatrix}$, $B = \begin{bmatrix}a & 1 \\ b & -1\end{bmatrix}$ and $(A + B)^2 = A^2 + B^2$ then

$a = 1, b = 4$

$a = -1, b = 4$

$a = 2, b = -3$

$a = 1, b = -4$

✅ Correct Option: 1

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