List of top Mathematics Questions on Matrices asked in GUJCET

If inverse matrix of \( A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix} \) is \( A^{-1} = \begin{bmatrix} a & \frac{3}{11} \\ \frac{1}{11} & b \end{bmatrix} \), then a + b = _____

If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix} \] then \( A^2 + B^2 = \underline{\hspace{2cm}} \)

If \( A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} \), then \( A^2 + I = \) _____

If \( A \) and \( B \) are skew-symmetric matrices of same order, then \( AB - BA \) is a _____

If \( A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} \) is such that \( A^2 = I \), then _____