If A is a square matrix such that $A^2 = A$ and I is the identity matrix of same order as A, then the matrix $(2I+A)^3 - 19A - 3I$ is equal to

Let $A = \begin{bmatrix} 1 & 2 & 1 \\ -1 & 3 & 2 \\ 2&4&1\end{bmatrix}$ and $M_{ij}$, $A_{ij}$ respectively denote the minor, co-factor of an element $a_{ij}$ of matrix A, then which of the following are true?

(A) $M_{22} = -1$

(B) $A_{23} = 0$

(C) $A_{32} = 3$

(D) $M_{23} = 1$

(E) $M_{32} = -3$

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With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$, which of the following are TRUE ?

A. |A|=125

B. A is a scalar matrix.

C. A is a diagonal matrix.

D. |A|=-125

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Match the LIST-I with LIST-II

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If A is an invertible matrix, then which of the following statement(s) is/are TRUE?

(A) $|A^{-1}| = |A|$

(B) $(A^{-1})^{-1} = A$

(C) $A^{-1} = \frac{adj A}{|A|}$

(D) $(A^T)^{-1} = (A^{-1})^T$

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If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$, then $|A|$ is

Let $A = \begin{bmatrix} 2 & -3 & 4 \\ 0 & 1 & 5 \\ -4 & 2 & 3 \end{bmatrix}$ and $a_{ij}$ be any element of matrix A, i, j ∈ {1,2,3}, then which of the following are TRUE?

(A) Minor of $a_{23} = 16$

(B) Minor of $a_{23} = -8$

(C) Cofactor of $a_{23} = -16$

(D) Cofactor of $a_{23} = 8$

(E) Cofactor of $a_{13} = 4$

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