If A is a square matrix such that $A^2 = A$ then which of the following statements are TRUE ? (Where I is an identity matrix of same order as A)

(A) $(I+A)^4 = I + 15A$

(B) $(I+A)^2 = I + 3A$

(C) $(I+A)^6 = I + 30A$

(D) $(I+A)^3 = I + 7A$

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Suppose that A, B and C are matrices of order $m \times n$, $n \times 5$ and $5 \times q$ respectively. The restriction on $m$, $n$ and $q$ so that AB-BC is defined are

If the matrix $\begin{bmatrix}3 & 2a & -5\\4 & 0 & b\\-5 & 3 & 10\end{bmatrix}$ is symmetric, then the value of $5a + 2b$ is

If A is a square matrix of order 3 and $|adj A| = 49$, then $|7A^{-1}|^2$

If $A = \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix}$ and $B = \begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix}$, then $A + B$ is equal to

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then

Consider the system of equation $x+y+3z=8$, $2x+y+bz=24$, $x+ay+3z=10$, then which of the following statements are True?

(A) The system of equations has a unique solution if $a=2, b=3$

(B) The system of equations is inconsistent if $a=1, b \in R$ be any real number.

(C) The system of equations is inconsistent if $a \neq 1$, and $b \neq 6$

(D) The system of equations has a unique solution if $a=4$ and $b=3$.

Choose the correct answer from the options given below: