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(B) Let $A$ be an $n 	imes n$ upper-triangular matrix,where $a_{ij} = 0$ for $i > j$. The adjoint of a matrix $A$,denoted by $adj(A)$,is the transpos

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upper triangular matrix

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(B) Let $A$ be an $n 	imes n$ upper-triangular matrix,where $a_{ij} = 0$ for $i > j$. The adjoint of a matrix $A$,denoted by $adj(A)$,is the transpose of the cofactor matrix $C = [C_{ij}]$. For an upper-triangular matrix,the cofactor $C_{ij}$ is zero if $i > j$. Specifically,the cofactor matrix $C$ will be a lower-triangular matrix because the elements above the diagonal involve determinants of submatrices that contain at least one row or column of zeros. Since $adj(A) = C^T$,the transpose of a lower-triangular matrix is an upper-triangular matrix. Therefore,$adj(A)$ is an upper-triangular matrix.

Let $A$ be a $n \times n$ matrix such that $A$ is an upper-triangular matrix. Then $adj(A) =$

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