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(A) A

(B) I–A

(C) I

(D) 3A

1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix.

5. If \(A=\begin{bmatrix}3&1 \\ -1&2\end{bmatrix}\), show that \(A^2-5A+7I=0\).

9. If \(A=\begin{bmatrix}α&β \\ γ &-α\end{bmatrix}\) is such that \(A^2=I\), then

(A) \(1+α^2+βγ=0\)

(B) \(1-α^2+βγ=0\)

(C) \(1-α^2-βγ=0\)

(D) \(1+α^2-βγ=0\).

10. If the matrix A is both symmetric and skew symmetric, then

(A) A is a diagonal matrix

(B) A is a zero matrix

(C) A is a square matrix

(D) None of these

11. If A is square matrix such that \(A^2=A\), then \((I+A)^3–7A\) is equal to

(A) A

(B) I–A

(C) I

(D) 3A